int frac{4}{x(ln x+1)^{2}} d x

Question

Accepted Answer

Step:1 ：(u = ln x + 1)Step:2 ：(frac{d u}{d x} = frac{1}{x})Step:3 ：(int frac{4}{x(u)^{2}} d x = 4 int frac{1}{u^2} d u)Step:4 ：(-4u^{-1} + C = -frac{4}{u} + C)Step:5 ：(-frac{4}{ln x + 1} + C)

Answer

Step: 1 ：(u = ln x + 1)Step: 2 ：(frac{d u}{d x} = frac{1}{x})Step: 3 ：(int frac{4}{x(u)^{2}} d x = 4 int frac{1}{u^2} d u)Step: 4 ：(-4u^{-1} + C = -frac{4}{u} + C)Step: 5 ：(-frac{4}{ln x + 1} + C)

$\int \frac{4}{x(\ln x+1)^{2}} d x$

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