Answer to Question #167810 in Calculus for Phyroe

Question

Evaluate the integral of Csc² (2-3x) dx

Answer 1

Solution:

$I=\int \csc^2 (2-3x)dx$ ...(i)

Put $2-3x=t$

$\Rightarrow 0-3=\dfrac{dt}{dx}$ [On differentiating]

$\Rightarrow dx=-\dfrac{dt}{3}$

Putting these values in (i), we get

$\Rightarrow I=\dfrac13\int(- \csc^2 t)dt$

$\Rightarrow I=\dfrac13\cot t+C$

$\Rightarrow I=\dfrac13\cot (2-3x)+C$ [Substituting value of $t$ back]