Mathematics

# $\displaystyle \int \frac{x^{9}}{(x^{2} + 4)^{6}} dx$ is equal to

##### ANSWER

$\displaystyle \frac{1}{40}\left ( 1 + x^{-2} \right )^{-5} + c$

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Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

Q1 Single Correct Hard
Evaluate $\displaystyle \int_{0}^{\pi /4}\frac{\cos x-\sin x}{10+\sin 2x}dx$
• A. $\displaystyle \frac{1}{3}\left (\tan^{-1} \frac{\sqrt{2}}{3}+\tan^{-1} \frac{1}{3} \right )$
• B. $\displaystyle \frac{1}{3}\left (\tan^{-1} \frac{\sqrt{1}}{3}-\cot^{-1} \frac{2}{3} \right )$
• C. $\displaystyle \frac{1}{3}\left ( \tan^{-1} \frac{\sqrt{1}}{3}-\cot^{-1} \frac{1}{3} \right )$
• D. $\displaystyle \frac{1}{3}\left ( \tan^{-1} \frac{\sqrt{2}}{3}-\tan^{-1} \frac{1}{3} \right )$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Resolve into partial fraction $\displaystyle \frac{7+x}{(1+x)(1+x^2)}$
• A. $\displaystyle \frac{5}{1+x}+\frac{4-3x}{1+x^2}$
• B. $\displaystyle \frac{3}{1+x}-\frac{4-3x}{1+x^2}$
• C. $\displaystyle \frac{5}{1+x}-\frac{4-3x}{1+x^2}$
• D. $\displaystyle \frac{3}{1+x}+\frac{4-3x}{1+x^2}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Find the value of $\displaystyle\int _{ 0 }^{ 2\pi }{ \sin ^{ 2 }{ x } \cdot \cos ^{ 4 }{ x } dx }$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium

$\displaystyle \int_{0}^{\pi}x.\sin^{3}xdx_{=}$
• A. $\displaystyle \frac{\pi}{3}$
• B. $\displaystyle \frac{\pi}{5}$
• C. $\displaystyle \frac{2\pi}{5}$
• D. $\displaystyle \frac{2\pi}{3}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
The value of $\displaystyle\int\limits_{1}^{e^2}\dfrac{dx}{x}$
• A. $1$
• B. $-1$
• C. $-2$
• D. $2$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020