Question

$\int \frac{1}{\sqrt{si{n}^{3}xcosx}}dx=$

• A. $\frac{-2}{\sqrt{tanx}}+c$
• B. $2\sqrt{tanx}+c$
• C. $\frac{2}{\sqrt{tanx}}+c$
• D. $-2\sqrt{tanx}+c$

Answer 1

The correct option is A $\frac{-2}{\sqrt{tanx}}+c$

$\int \frac{1}{\sqrt{si{n}^{3}xcosx}}dx=\int \frac{1}{si{n}^{2}x\sqrt{cotx}}dx=\int \frac{cose{c}^{2}x}{\sqrt{cotx}}dx=-2\sqrt{cotx}+c=-\frac{2}{\sqrt{tanx}}+c$