Integrals of the form : f'(x)ef(x)

In this tutorial you are shown how to do integrals of the above form

Formulae to remember:

  • \displaystyle\int {f'(x){e^{f(x)}}} dx = e^{f(x)} + c

The examples used are:

  1. \displaystyle\int {2x{e^{x^2}}} dx
  2. \displaystyle\int {x{e^{x^2}}} dx
  3. \displaystyle\int {4{e^{4\sin x}}\cos x} dx
  4. \displaystyle\int {e^{4\sin x}\cos x} dx
  5. \displaystyle\int {3x{e^{x^2}}} dx
  6. \displaystyle\int {e^{2 \sin x} \cos x} dx
  7. \displaystyle\int {5x^2{e^{4x^3}}} dx
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