Question

$\int cose{c}^{n}x\cdot cotxdx,(n\ne 0)=$

• A. $\frac{cose{c}^{n}x}{n}+c$
• B. $\frac{cose{c}^{n+1}x}{n+1}+c$
• C. $-\frac{cose{c}^{n+1}x}{n+1}+c$
• D. $-\frac{cose{c}^{n}x}{n}+c$

Answer 1

The correct option is D $-\frac{cose{c}^{n}x}{n}+c$

$\int cose{c}^{n}x.cotx.dx$

$\int \frac{cosx}{si{n}^{n+1}x}dx$

$dsinx=cosx.dx$

$\int \frac{dsinx}{si{n}^{n+1}x}sinx=t$

$\int \frac{dt}{t^{n+1}}=\frac{t^{-n}}{-n}+c$

$=\frac{-1}{n}cose{c}^{n}x+c$

$\int cose{c}^{n}x.cotxdx.=-\frac{cose{c}^{n}x}{n}+c$