Question

$\int \frac{1}{\sqrt{x}(1+\sqrt{x})}dx=$

• A. $\log |1+\sqrt{x}|+c$
• B. $2\log |1+\sqrt{x}|+c$
• C. $-\log |1+\sqrt{x}|+c$
• D. $\frac{1}{(1+\sqrt{x})}+c$

Answer 1

Answer: (B)

$2\log |1+\sqrt{x}|+c$

$let\sqrt{x}=t$

$\frac{1}{2}{x}^{-\frac{1}{2}}dx=dt$

$\frac{1}{\sqrt{x}}.dx=2dt$

$\int \frac{2dt}{(1+t)}=2log(1+t)+c$

$=2log(1+\sqrt{x})+c$

$\int \frac{1}{\sqrt{x}(1+\sqrt{x})}dx=2log(1+\sqrt{x})+c\cdot$