Mathematics

# Evaluate the following integrals:$\displaystyle \int { \cot ^{ n }{ x }\ cosec ^{ 2 }{ x } } dx,n\neq -1$

##### SOLUTION
$\displaystyle\int{{\cot}^{n}{x}\,{cosec}^{2}{x}dx}$

$=\displaystyle\int{{\left(\cot{x}\right)}^{n}{cosec}^{2}{x}dx}$

Let

$t=\cot{x}\Rightarrow\,dt=-{cosec}^{2}{x}dx$

$=-\displaystyle\int{{t}^{n}dt}$

$=-\dfrac{{t}^{n+1}}{n+1}+c$

$=-\dfrac{{\cot}^{n+1}{x}}{n+1}+c$ where $t=\cot{x}$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
Solve:
$\displaystyle \int_{0}^{1} \ x+x^2 dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\displaystyle\int \dfrac{\sqrt{\tan x}}{\sin x\cos x}dx$ is equal to?
• A. $2\sqrt{\cot x}+C$
• B. $\dfrac{\sqrt{\tan x}}{2}+C$
• C. $\sqrt{\tan x}+C$
• D. $2\sqrt{\tan x}+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int \frac{2\ sinx + 3 \ cosx}{3 \ sinx + 4\ cosx} \;dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate the given integral.
$\displaystyle \int { \left( \cfrac { 2-x }{ { (1-x) }^{ 2 } } \right) } { e }^{ x }dx$

$\int \frac{1}{1+x}\;dx$