Integrals of exponential and logarithmic functions formulas

$\int e^x dx = e^x + C$

$ \int a^x dx = \dfrac{a^x}{\ln a} + C $

$ \int e^{ax} dx = \dfrac{e^{ax}}{a}+C$

$ \int x e^{ax}dx = \dfrac{e^{ax}}{a^2}(ax-1)+C $

$ \int \ln x dx = x\ln x - x + C$

$ \int \dfrac{dx}{x\ln x} = \ln|\ln x| + C $

$ \int x \ln x dx = x^2 \left[\dfrac{\ln x}{2}-\dfrac{1}{4}\right] + C $

$ \int x^n \ln x dx = x^{n+1} \left[\dfrac{\ln x}{n+1}-\dfrac{1}{(n+1)^2}\right] + C $

$\int e^{ax} \sin bx dx = \dfrac{a\sin bx - b \cos bx}{a^2+b^2} e^{ax} + C $

10.

$\int e^{ax} \cos bx dx = \dfrac{a\cos bx - b \sin bx}{a^2+b^2} e^{ax} + C $