Mathematics

# Solve : $\int x . \sin^2 x \, dx$

$\dfrac {x^2}{4}-x\dfrac {\sin 2x}{4}-\dfrac {\cos 2x}{8}$

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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 Hard
$\displaystyle \int {\frac{{dx}}{{(x + p)\sqrt {(x - p)(x - q)} }}}$ is equal to
• A. $\frac{2}{{p - q}}\sqrt {\frac{{x - p}}{{x - q}} + c}$
• B. $- \frac{2}{{p - q}}\sqrt {\frac{{x - q}}{{x - p}} + c}$
• C. None of these
• D. $\frac{1}{{\sqrt {\left( {x - p} \right)(x - q)} }} + c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Solve $\displaystyle \int \sec(\log x)[1+\tan(\log x)]dx$
• A. $\displaystyle \frac{x}{2}\sec(\log x)+c$
• B. $\displaystyle -x\sec(\log x)+c$
• C. $\displaystyle \frac{-x}{2} \sec(\log x)+c$
• D. $\displaystyle x\sec(\log x)+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
$\int {\frac{{{e^x}}}{x}\,\left( {1 + x.lnx} \right)} \,dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integral:
$\displaystyle\int^{\pi/2}_0\dfrac{\sin x}{\sqrt{1+\cos x}}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \int_1^{32}\dfrac{dx}{x^{1/5}\sqrt{1+x^{4/5}}}$
• A. $\dfrac{2}{5}(\sqrt{17}-\sqrt{2})$
• B. $\dfrac{5}{2}(\sqrt{17}-\sqrt{2})$
• C. $\dfrac{5}{2}(\sqrt{17}+\sqrt{2})$
• D. $\dfrac{2}{5}(\sqrt{17}+\sqrt{2})$