Integrals

 

Indefinite Integral

Method of substitution

∫f(g(x))⋅g′(x)dx=∫f(u)du

Integration by parts

∫f(x)⋅g′(x)dx=f(x)⋅g(x)−∫g(x)⋅f′(x)dx

Integrals of Rational and Irrational Functions

∫xndx=xn+1n+1+C,n≠1

∫1xdx=ln|x|+C

∫cdx=c⋅x+C

∫xdx=x22+C

∫x2dx=x33+C

∫1x2dx=−1x+C

∫x√dx=2⋅x⋅x√3+C

∫11+x2dx=arctanx+C

∫11−x2−−−−−√dx=arcsinx+C