Exponential and log integrals

Integral of eˣ \int e^x\,dx = e^x + C The integral of eˣ is eˣ + C. See why eˣ is its own antiderivative, a graph of the area, definite and improper integrals and worked examples. Integral of e²ˣ \int e^{2x}\,dx = \frac{1}{2}e^{2x} + C The integral of e^(2x) is ½e^(2x) + C, and in general ∫e^(kx) dx = (1/k)e^(kx) + C. See the substitution, a graph and worked examples. Integral of e⁻ˣ \int e^{-x}\,dx = -e^{-x} + C The integral of e^(−x) is −e^(−x) + C. See the substitution, why the area from 0 to infinity is 1, a graph and examples like x e^(−x). Integral of e^(x²) \int e^{-x^2}\,dx = \frac{\sqrt{\pi}}{2}\,\operatorname{erf}(x) + C e^(x²) and e^(−x²) have no elementary antiderivative. Learn the erf and erfi functions, the power series answer and why ∫e^(−x²) over ℝ is √π. Integral of 2ˣ \int 2^x\,dx = \frac{2^x}{\ln 2} + C The integral of 2ˣ is 2ˣ/ln 2 + C, and ∫aˣ dx = aˣ/ln a + C. See the derivation from e^(x ln a), a graph, definite integrals and examples. Integral of ln x \int \ln x\,dx = x\ln x - x + C The integral of ln x is x ln x − x + C. See the integration by parts steps, a check by differentiating, a graph and examples like ln(2x) and (ln x)². Integral of 1/(x ln x) \int \frac{1}{x\ln x}\,dx = \ln\lvert\ln x\rvert + C The integral of 1/(x ln x) is ln|ln x| + C. See the u = ln x substitution, why its improper integral diverges, a graph and worked examples.