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Evaluate int(1+x^(2)log(e)x)/(x+x^(2)lo...

Evaluate `int(1+x^(2)log_(e)x)/(x+x^(2)log_(e)x)dx`

Text Solution

Verified by Experts

The correct Answer is:
`log_(e)x+x-log_(e)|1+xlog_(e)x|+C`
`int(1+x^(2)log_(e)x)/(x(1+xlog_(e)x))dx=int((1+x)/(x)-(1+log_(e)x)/(1+xlog_(e)x))dx`
`=int((1+x)/(x))dx+int((1+log_(e)x)')/(1+xlog_(e)x)dx `
`=log_(e)x+x-log_(e)|1+xlog_(e)x|+C`
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