Answer to Question #88343 in Calculus for Shivam Nishad

Question

Evaluate the following integrals:
ii) ∫ ln(x+1)/(√x+1)dx

Answer 1

Solution. We use the integration formula in parts

$$\int \frac {ln(x+1)} {\sqrt{x+1}}dx= \begin{vmatrix} u=ln(x+1) & dv=\frac {dx} {\sqrt{x+1}} \\ du=\frac {dx}{x+1} & v=2\sqrt{x+1} \end{vmatrix}=$$

$$=2\sqrt{x+1}*ln(x+1)-\int \frac{2\sqrt{x+1}}{x+1}dx=$$

$$=2\sqrt{x+1}*ln(x+1)-\int \frac{2} {\sqrt{x+1}}dx=$$

$$=2\sqrt{x+1}*ln(x+1)-4\sqrt{x+1}+C$$

where C is constant.

Answer.

$$2\sqrt{x+1}*ln(x+1)-4\sqrt{x+1}+C$$

where C is constant.