Mathematics

# Evaluate $\int { { cosec }^{ 4 }x\ \ dx\quad }$

$-\cot { x- } \dfrac { \cot ^{ 3 }{ x } }{ 3 } +c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Evaluate $\int e^x sin \,e^x dx$ on R

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle \int_{0}^{\pi } \frac{x\tan x}{\sec x+\cos x} \:dx$ is
• A. $\displaystyle \frac{\pi ^2}{2}$
• B. $\displaystyle \frac{3\pi ^2}{2}$
• C. $\displaystyle \frac{\pi ^2}{3}$
• D. $\displaystyle \frac{\pi ^2}{4}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int \frac{2x^{4}+x^{3}-4x^{2}+4x+2}{(x^{2}+4)(x^{2}-1)^{2}}dx$
• A. $\displaystyle \tan ^{-1}\frac{x}{2}+\frac{1}{2}\cdot \frac{1}{x^{2}-1}$
• B. $\displaystyle \tan ^{-1}\frac{x}{2}-\frac{1}{3}\cdot \frac{1}{x^{2}-1}$
• C. $\displaystyle \tan ^{-1}\frac{x}{2}-\frac{1}{2}\cdot \frac{1}{x^{2}+1}$
• D. $\displaystyle \tan ^{-1}\frac{x}{2}-\frac{1}{2}\cdot \frac{1}{x^{2}-1}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate : $\displaystyle \int { \dfrac { 1 }{ { 2x }^{ 2 }+x+1 } } dx$

$\sqrt{2}\displaystyle \int _{ 0 }^{ 2\pi }{ \sqrt { 1-\sin { x } } dx } =$