Inverse trig integrals

Integral of 1/(1+x²) \int \frac{1}{1+x^2}\,dx = \arctan x + C The integral of 1/(1+x²) is arctan x + C. See why with a tan substitution, the 1/(a²+x²) version, a graph and worked examples. Integral of 1/√(1−x²) \int \frac{1}{\sqrt{1-x^2}}\,dx = \arcsin x + C The integral of 1/√(1−x²) is arcsin x + C. See the sine substitution, the 1/√(a²−x²) version, a graph, definite integrals and examples. Integral of √(1−x²) \int \sqrt{1-x^2}\,dx = \frac{1}{2}\left(x\sqrt{1-x^2} + \arcsin x\right) + C The integral of √(1−x²) is ½(x√(1−x²) + arcsin x) + C. Learn the trig substitution, the link to the area of a circle and worked examples. Integral of arctan x \int \arctan x\,dx = x\arctan x - \frac{1}{2}\ln(1+x^2) + C The integral of arctan x is x arctan x − ½ ln(1+x²) + C. See the integration by parts steps, a check, definite integrals and examples. Integral of arcsin x \int \arcsin x\,dx = x\arcsin x + \sqrt{1-x^2} + C The integral of arcsin x is x arcsin x + √(1−x²) + C. Learn the integration by parts steps, the arccos version, a graph and worked examples.