# Georgia Tech MATH 1552 Integral Calculus: Study Guide and Practice

> A study guide for Georgia Tech MATH 1552 (Integral Calculus): integrals, integration techniques, improper integrals and infinite series, with practice.

Source: https://practicecalculus.com/courses/georgia-tech-math-1552
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 1552
- **Credits:** 4 credit hours
- **Covers:** Definite and indefinite integrals, techniques of integration, improper integrals, infinite series and applications
- **Credit restrictions:** No credit for both MATH 1552 and MATH 1502, MATH 1504, MATH 1512 or MATH 1555
- **Practice here:** [Calculus 1](/learn/calculus-1) integrals units plus [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 1552 is Georgia Tech's 4-credit-hour course in integral calculus.
- It starts with definite and indefinite integrals, so it covers the integral half of a typical Calculus 1 course as well as Calculus 2.
- Techniques of integration, improper integrals and infinite series make up the core of the course.
- It pairs with MATH 1551 (Differential Calculus), which handles limits and derivatives.

**Georgia Tech MATH 1552** is Integral Calculus, a 4-credit-hour course that covers everything about integration in one variable, from the first antiderivative to infinite series. It is the integral counterpart to MATH 1551 (Differential Calculus). This guide maps every MATH 1552 topic to free practice, so you can learn each technique by solving problems with instant feedback.

## What MATH 1552 covers

According to the Georgia Tech catalog, MATH 1552 covers definite and indefinite integrals, techniques of integration, improper integrals, infinite series and applications. Credit is not awarded for both MATH 1552 and MATH 1502, MATH 1504, MATH 1512 or MATH 1555.

That scope is wider than a standard **Calculus 2** course. It begins with material many universities teach at the end of **Calculus 1** (antiderivatives, Riemann sums and the Fundamental Theorem of Calculus), then moves through the integration techniques, improper integrals and series of Calculus 2.

## MATH 1552 topic map

| MATH 1552 topic | Practice | Read |
| --- | --- | --- |
| Indefinite integrals | [Undoing derivatives](/learn/calculus-1/integrals/undoing-derivatives) | [Antiderivatives](/blog/antiderivatives), [reverse power rule](/rules/reverse-power-rule) |
| Definite integrals and Riemann sums | [Area with rectangles](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums](/blog/riemann-sums), [definite integral properties](/rules/definite-integral-properties) |
| Fundamental Theorem of Calculus | [Evaluating definite integrals](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus), [FTC part 1](/theorems/fundamental-theorem-of-calculus-part-1) |
| Substitution | [U-substitution](/learn/calculus-1/integrals/u-substitution) | [u-substitution](/blog/u-substitution) |
| Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts](/blog/integration-by-parts) |
| Trig integrals and trig substitution | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions](/blog/partial-fractions) |
| Improper integrals | [Integrands that blow up](/learn/calculus-2/improper-integrals-and-applications/infinite-discontinuities) | [Improper integrals](/blog/improper-integrals) |
| Applications of integration | [Volumes with disks](/learn/calculus-1/applications-of-integrals/volumes-disks) | [Area between curves](/blog/area-between-curves), [volumes of revolution](/blog/volumes-of-revolution) |
| Sequences and series | [Geometric series](/learn/calculus-2/sequences-and-series/geometric-series) | [Geometric series](/blog/geometric-series), [nth-term test](/rules/nth-term-test) |
| Convergence tests | [Choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) | [Convergence tests](/blog/convergence-tests), [ratio test](/rules/ratio-test) |
| Power and Taylor series | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials) | [Power series](/blog/power-series), [Taylor series](/blog/taylor-series) |

## MATH 1552 in the Georgia Tech calculus courses

| Course | Credit hours | Focus |
| --- | --- | --- |
| MATH 1551 (Differential Calculus) | 2 | Limits of functions and sequences, derivatives and applications |
| MATH 1552 (Integral Calculus) | 4 | Integrals, integration techniques, improper integrals, series |
| MATH 2550 (Introduction to Multivariable Calculus) | 2 | Several variables, without vector calculus |
| MATH 2551 (Multivariable Calculus) | 4 | Several variables, including vector analysis |

If derivatives feel rusty, review the [MATH 1551 guide](/courses/georgia-tech-math-1551). For calculus in several variables, continue with the [MATH 2551 guide](/courses/georgia-tech-math-2551).

## Example problems at the MATH 1552 level

**1. A substitution integral.** Let $u = x^2 + 1$, so $du = 2x\,dx$:

$$\int 2x(x^2 + 1)^3\,dx = \int u^3\,du = \frac{(x^2 + 1)^4}{4} + C$$

**2. Partial fractions.** Since $\frac{1}{x(x + 1)} = \frac{1}{x} - \frac{1}{x + 1}$,

$$\int \frac{1}{x(x + 1)}\,dx = \ln|x| - \ln|x + 1| + C = \ln\left|\frac{x}{x + 1}\right| + C$$

**3. The ratio test.** For $\sum_{n=1}^{\infty} \frac{n}{2^n}$,

$$\lim_{n \to \infty} \frac{(n + 1)/2^{n+1}}{n/2^n} = \lim_{n \to \infty} \frac{n + 1}{2n} = \frac{1}{2} < 1$$

so the series converges.

## How to do well in Georgia Tech MATH 1552

- **Learn to pick the technique.** The hard part of integration is deciding what to try. Our [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) lesson trains exactly that.
- **Check by differentiating.** Every indefinite integral can be verified by taking its derivative, a habit that catches most sign and constant errors.
- **Build a series decision list.** Know when to use the nth-term, comparison, integral, alternating and ratio tests. The [convergence tests guide](/blog/convergence-tests) lays them side by side.
- **Keep formulas close.** The [calculus formula sheet](/formulas) collects integrals and series on one page.
- **Practice under exam conditions** with [practice exams](/practice), and review [common calculus mistakes](/blog/common-calculus-mistakes) first.

> **Tip:** if a series term looks like $\frac{\text{polynomial}}{\text{exponential}}$, reach for the [ratio test](/rules/ratio-test) first. The exponential almost always wins.

## Frequently asked questions

### What is MATH 1552 at Georgia Tech?

MATH 1552 is Integral Calculus, a 4-credit-hour course. The catalog lists definite and indefinite integrals, techniques of integration, improper integrals, infinite series and applications.

### Is MATH 1552 the same as Calculus 2?

Mostly, but it also starts earlier. Because Georgia Tech teaches derivatives separately in MATH 1551, MATH 1552 begins with antiderivatives and the definite integral, which many schools teach at the end of Calculus 1, then continues into integration techniques and series.

### Is MATH 1552 hard?

It covers a lot: the whole of integration plus infinite series. Series in particular feel different from earlier calculus because you decide whether a sum converges rather than computing an answer. Regular mixed practice is the most reliable way through it.

### How should I prepare for MATH 1552?

Make sure derivatives are automatic, especially the chain rule, since every antiderivative is a derivative read backwards. Then practice basic antiderivatives and u-substitution before the course starts.

### What should I study after MATH 1552?

The catalog lists MATH 2551 (Multivariable Calculus) and MATH 2550 (Introduction to Multivariable Calculus) for calculus in several variables. Check your degree requirements for which one applies to you.