Mathematics

# Integrate:$\int \dfrac { x ^ { 4 } } { x ^ { 2 } + 1 }$ dx =

$\dfrac { x ^ { 3 } } { 3 } - x + \tan ^ { - 1 } x + c$

##### SOLUTION
$\int \dfrac{x^{4}}{x^{2}+1}dx=\int \dfrac{x^{4}+1-1}{x^{2}+1}dx=\int (\dfrac{x^{4}-1}{x^{2}+1}+\dfrac{1}{x^{2}+1})dx$

$=\int ((x^{2}-1)+\dfrac{1}{x^{2}+1})dx$

$= \dfrac{x^{3}}{3}-x+tan^{-1}x+c$

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

#### Realted Questions

Q1 Single Correct Hard
The value of the integral $\displaystyle \int_0^1 \dfrac{x^{\alpha}-1}{\log x}dx$ is
• A. $2\log (\alpha+1)$
• B. $3\log \alpha$
• C. none of these
• D. $\log (\alpha+1)$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate:
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1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value of $\displaystyle \int_{0}^{2}[x^2-x+1]dx$ (where,[.] denotes the greatest integer function ) is equal to
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• B. $\dfrac{1+\sqrt{5}}{2}$
• C. $\dfrac{1-\sqrt{5}}{2}$
• D. $\dfrac{5-\sqrt{5}}{2}$
• E. $\dfrac{5-\sqrt{5}}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium

Evaluate:$\displaystyle\frac { 1 } { 15 } \int \frac { d t } { 4 + t ^ { 2 } } + \frac { 4 } { 15 } \int \frac { 6 d t } { 1 + 4 t ^ { 2 } }$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium

lf $f(\mathrm{x})$ is an even function, and $n\in N$, then $\displaystyle \int_{-\pi}^{\pi}f(x) \sin nx\ dx=$
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