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Make substitutions in the integration by parts formula and simplify.

Make substitutions in the integration by parts formula and simplify.-example-1
User Severiano
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1 Answer

19 votes
19 votes

For integral by parts

Your exercise inform:

Therefore


\begin{gathered} u=x^n \\ v=(1)/(a)\cdot e^(ax) \\ du=nx^(n-1) \end{gathered}

Applying the formula


\begin{gathered} uv-\int vdu \\ x^n\cdot(1)/(a)\cdot e^(ax)-\int (1)/(a)\cdot e^(ax)\cdot nx^(n-1) \end{gathered}

Answer:


(x^n\cdot(1)/(a)\cdot e^(ax))-\int ((1)/(a)\cdot e^(ax)\cdot nx^(n-1))

Make substitutions in the integration by parts formula and simplify.-example-1
Make substitutions in the integration by parts formula and simplify.-example-2
User Sebastian Stumpf
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2.9k points