Mathematics

# The value of $\displaystyle \int \dfrac {x^{2}}{x+2}dx$ equals

$\dfrac {x^{3}}{3}+x^{2}+4x-8\log |x+2|+c$

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

#### Realted Questions

Q1 Single Correct Medium
$\int_{0}^{\frac{1}{2}}\frac{xsin^{-1}x}{\sqrt{1-x^{2}}}dx$ is equal to
• A. $\frac{1}{2}-\frac{\pi }{2\sqrt{3}}$
• B. $\frac{1}{2}+\frac{\pi }{4\sqrt{3}}$
• C. $\frac{1}{2}+\frac{\pi }{4\sqrt{3}}$
• D. $\frac{1}{2}+\frac{\pi }{2\sqrt{3}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integrate the following function with respect to $x$
$x^{2}.\cos{(x^{3})}\sqrt{\sin^{7}{(x^{3})}}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle I = \int \frac {x^2}{(x - a)(x - b)} dx$, then I equals
• A. $\displaystyle x + \frac {1}{a - b} \log \left | \frac {x - a}{x - b} \right | + C$
• B. $\displaystyle x + \frac {1}{a - b} \log \left | \frac {x - a}{x - b} \right |^{a^2 + b^2} + C$
• C. none of these
• D. $\displaystyle x + \frac {1}{a - b} \{a^2 \log |x - a| - b^2 \log |x - b| \} + C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Multiple Correct Hard
Let $f\left ( x \right )$ be a non-constant twice differentiable function defined on $\left ( -\infty , \infty \right )$ such that $f\left ( x \right )= f\left ( 1-x \right )$ and $f{}'\displaystyle \left ( \frac{1}{4} \right )= 0$. Then which of the following is/are true?
• A. $f'\left ( x \right )$ vanishes at least twice on $\left [ 0, 1 \right ]$
• B. $f'\left (\dfrac12 \right )= 0$
• C. $\displaystyle \int_{-\frac12}^{\frac12}f\left ( x+\dfrac12 \right )\sin x\: dx= 0$
• D. $\displaystyle \int_{0}^{\frac12}f\left ( t \right )e^{\sin \pi }dt= \displaystyle \int_{\frac12}^{1}f\left ( 1-t \right )e^{sin\pi }dt$

$\int \frac{1}{1+x}\;dx$