Mathematics

# The integral $\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$ is equal to?(Here C is a constant of integration)

$\log_e\left|\dfrac{x^3+1}{x}\right|+C$

##### SOLUTION
$\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$

$\displaystyle\int \dfrac{2x-\dfrac{1}{x^2}}{x^2+\dfrac{1}{x}}dx$

$x^2+\dfrac{1}{x}=t$

$\left(2x-\dfrac{1}{x^2}\right)dx=dt$

$\displaystyle\int \dfrac{dt}{t}=ln (t)+C$

$=ln \left(x^2+\dfrac{1}{x}\right)+C$

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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 Medium
If $f\left ( x \right )= A\sin \left ( \dfrac {\pi x}{2} \right )\: +\: B,f{}'\left ( \dfrac 12 \right )= \sqrt{2}$ and $\displaystyle \int_{0}^{1}f\left ( x \right )dx= \displaystyle \frac{2A}{\pi }$,
then the constants $A$ and $B$ are
• A. $A=\dfrac {\pi}{2}, B=\dfrac {\pi}{2}$
• B. $A=\dfrac {2}{\pi}, B=3\pi$
• C. $A=0, B=-4\pi$
• D. $A=\dfrac {4}{\pi}, B=0$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int _{ 0 }^{ { \pi }/{ 2 } }{ \frac { \cos { x } -\sin { x } }{ 1+\cos { x } \sin { x } } } dx$ is equal to:
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• C. $\displaystyle \frac { \pi }{ 6 }$
• D.

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
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