Integral of Exponential and Logarithmic Functions

Posted In: Mathematics
  1. $∫e^x\ dx=e^x+c$
  2. $∫a^x\ dx={a^x}/{ln\ a}+c$
  3. $∫e^{ax}\ dx=e^{ax}/a+c$
  4. $∫xe^{ax}\ dx=e^{ax}/a^2(ax-1)+c$
  5. $∫ln\ x\ dx=x\ ln\ x-x+c$
  6. $∫{dx}/{x\ ln\ x}=ln|ln\ x|+c$
  7. $∫x^n\ ln\ x\ dx=x^{n+1}[{ln\ x}/{n+1}-1/(n+1)^2]+c$
  8. $∫e^{ax}\ sin\ bx\ dx={a\ sin\ bx-b\ cos\ bx}/{a^2+b^2}e^{ax}+c$
  9. $∫e^{ax}\ cos\ bx\ dx={a\ cos\ bx+b\ sin\ bx}/{a^2+b^2}e^{ax}+c$

Post Tags: Integration


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