# Integral calculus - Integrals of exponential and logarithmic functions

1. $\int e^xdx=e^x+C$
2. $\int a^xdx={z^x \over In \, a} +C$
3. $\int e^{ax}dx= {e^{ax} \over a}+C$
4. $xe^{ax}dx= {e^{ax} \over a^2}(ax-1)+C$
5. $\int In \,x \, dx= x\,In\,x-x+C$
6. $\int {dx \over x \, In \, x}= In |In \, x|+C$
7. $\int x^n\, In \,x\,dx=x^{n+1} \bigg [ {In\, x \over n+1}- {1 \over (n+1)^2} \bigg ]+C$
8. $\int e^{ax}sin \, bx\, dx = {a\, sin \,bx-b\,cos \, bx \over a^2+b^2 }e^{ax}+C$
9. $\int e^{ax}cos \, bx\, dx = {a\, cos \,bx\,+\,b\,sin \, bx \over a^2+b^2 }e^{ax}+C$