The value of ∫$$(x+1)x1+xexdx$$ is

Correct option is 3log⁡xex1+xex+C

Questions

The value of $\int \frac{(x + 1)}{x (1 + x e^{x})} d x$ is

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log⁡1+xex+x+C

12log⁡x1+xexx+1+C

log⁡xex1+xex+C

log⁡(x+1)ex1+xex+C

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detailed solution

Correct option is C

Write the integrand as 1x+1−(x+1)ex1+xexSo the given integral is equal tolog⁡x+x−log⁡1+xex+C=log⁡x+log⁡ex−log⁡1+xex+C=log⁡xex1+xex+C.

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The value of ∫(x+1)x1+xexdx is

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The value of $\int \frac{(x + 1)}{x (1 + x e^{x})} d x$ is