Integrate the following functions- - x logsin x d x

∫ cot x log sin x dx. Let log sin x =t ⇒1/sin x× cos x =dt/dx ⇒ cot x =dt/dx⇒ dx =dt/cot x ∴∫ cot x log sin x dx =∫ cot x.t dt/cot x=∫ t dt =t^2/2+C =(log sin ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Properties Derived from Trigonometric Identities

Integrate the...

Question

Integrate the following functions.
$\int$ cot x log sin x dx.

Open in App

Solution

$\int$ cot x log sin x dx.
Let log sin $x = t \Rightarrow \frac{1}{s i n x} \times c o s x = \frac{d t}{d x}$
$\Rightarrow c o t x = \frac{d t}{d x} \Rightarrow d x = \frac{d t}{c o t x} ∴ \int c o t x l o g s i n x d x = \int c o t x . t \frac{d t}{c o t x} = \int t d t = \frac{t^{2}}{2} + C = \frac{(l o g s i n x)^{2}}{2} + C$

Suggest Corrections

Integrate the following functions. ∫ cot x log sin x dx.

∫ cot x log sin x dx. Let log sin x=t⇒1sinx×cosx=dtdx ⇒cotx=dtdx⇒dx=dtcotx∴∫cot x log sin xdx=∫cot x.tdtcotx=∫tdt=t22+C=(log sinx)22+C

Integrate the following functions.
$\int$ cot x log sin x dx.