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Grade 12Integral Calculus

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

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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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