Question

Find the integral of the given function w.r.t x

$y=sin6x+10se{c}^{2}x-cosecxcotx$

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$y=sin6x+10se{c}^{2}x-cosecxcotx$

$\Rightarrow \int (sin6x+10se{c}^{2}x-cosecxcotx)dx$

$\Rightarrow \int \left(sin6x\right)dx+\int \left(10se{c}^{2}x\right)dx-\int \left(cosecxcotx\right)dx$

$6x=t\Rightarrow 6dx=dt\Rightarrow dx=\frac{dt}{6}$

$\Rightarrow \int \frac{\left(sint\right)dt}{6}+10tanx+c_1-(-cosecx)+c_2$

$\Rightarrow \frac{-cos\left(t\right)}{6}+c_o+10tanx+c_1+cosecx+c_2$

$\Rightarrow \frac{-cos6x}{6}+10tanx+cosecx+c$