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. \(\int e^{ax}cos \, bx\, dx = {a\, cos \,bx\,+\,b\,sin \, bx \over a^2+b^2 }e^{ax}+C\)