Mathematics

# Prove that:$\displaystyle \int \dfrac {(\log x)^{2}}{x}dx$

##### SOLUTION
$I = \int \frac{(logx)^{2}}{x}dx$ let logx=t
$\Rightarrow \frac{1}{x}dx=dt$
$\Rightarrow I=\int t^{2}dt=\frac{t^{3}}{3}+c=\frac{(logx)^{3}}{3}+c$

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

#### Realted Questions

Q1 Single Correct Hard
Solve $\displaystyle \int\frac{dx}{\sqrt{x}+\sqrt[4]{x}}$
• A. $2 \sqrt{x}+4\sqrt[4]{x}+4\log(1 +\sqrt[4]{x})+c$
• B. $2 \sqrt{x}+2\sqrt[4]{x}+4\log(1 +\sqrt[4]{x})+c$
• C. $\sqrt{x}+3\sqrt[4]{x}-2\log(x+1)+c$
• D. $2 \sqrt{x}-4\sqrt[4]{x}+4\log(1 +\sqrt[4]{x})+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evalue: $\displaystyle \int^{\pi}_{0} \left(sin^2\left(\dfrac{x}{2}\right)-cos^2\left(\dfrac{x}{2}\right)\right)dx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate $\displaystyle\int^{\pi/2}_0(\sqrt{\sin x}\cos x)^3dx$
• A. $\dfrac{2}{9}$
• B. $\dfrac{2}{15}$
• C. $\dfrac{5}{2}$
• D. $\dfrac{8}{45}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate : $\displaystyle \int e^x \frac {(2-x)}{(1-x)^2}dx$

$\sqrt {\dfrac{x^2-a^2}{x}}dx.$