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Evaluate the following integrals​

Evaluate the following integrals​-example-1
User Ernie
by
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1 Answer

4 votes

Answer:


I = (1)/(8) e^(4x^2) + C

Explanation:

This can be solved using substitution method. Let us work it out.


Let \: I = \int xe^(4x^2) dx


\implies \: I = \int e^(4x^2) xdx


Put \:4x^2 = t


\implies 8x dx = dt


\implies x dx = (1)/(8)dt


\implies \: I = \int e^(t) (1)/(8)dt


\implies \: I = (1)/(8) \int e^(t)dt


\implies \: I = (1)/(8) e^(t) + C


\implies \: I = (1)/(8) e^(4x^2) + C


\implies \: \int xe^(4x^2) dx = (1)/(8) e^(4x^2) + C

User Mistiru
by
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