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evaluate the following integral ∫ x + 1 / x(x + log x) dx

evaluate the following integral
∫ x + 1 / x(x + log x) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:

Hello student,
Please find the answer to your question below

I = \int (x+\frac{1}{x(1+logx)})dx
I = \int xdx+\int \frac{1}{x(1+logx)}dx
I = \frac{x^2}{2}+\int \frac{1}{x(1+logx)}dx
logx + 1 = t
\frac{dx}{x} = dt
I = \frac{x^2}{2} + \int \frac{dt}{t}
I = \frac{x^2}{2} + log(t) + c
I = \frac{x^2}{2} + log(logx+1) + c


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