Mathematics

# $\displaystyle \int cosec^{n}x\cdot cotxdx,(n\neq 0)=$

$-\displaystyle \dfrac{cosec^{n}x}{n}+c$

##### SOLUTION
$\int cosec^{n}x.cot x.dx$

$\int \dfrac{cos x}{sin^{n+1}x}dx$

$d sin x = cos x.dx$

$\int \dfrac{d sin x}{sin^{n+1}x} sin x=t$

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

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

$\int cosec^{n}x.cotx dx. =-\dfrac{cosec^{n}x}{n}+c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Hard
The value of integral $\displaystyle \int \frac{\left(\sqrt{1+x^{2}}+x \right)^{n}}{\sqrt{1+x^{2}}}dx$, is
• A. $\displaystyle \frac{1}{n}\left ( \sqrt{1+x^{2}}+x \right )^{n-1}+c$
• B. $\displaystyle \frac{1}{n-1}\left ( \sqrt{1+x^{2}}+x \right )^{n-1}+c$
• C. $\displaystyle \frac{1}{n-1}\left ( \sqrt{1+x^{2}}+x \right )^{n}+c$
• D. $\displaystyle \frac{1}{n}\left ( \sqrt{1+x^{2}}+x \right )^{n}+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integral of $\displaystyle \frac{(4x^{2}-2\sqrt{x})}{x} +\frac{1}{1+x^{2}}-5 co\sec ^{2}x$ is

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate: $\displaystyle \int_{0}^{1} \ x+x^2 dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Simplify:
$\int {x{{\tan }^{ - 1}}xdx}$

$\displaystyle\int\dfrac{x}{\sqrt{3x^2+4}}dx$.