Mathematics

# Solve $\displaystyle \int {\frac{x}{{1 - {x^3}}}dx}$

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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 Medium
$\int_{0}^{1}\dfrac{\sin t}{1+t}dt=\alpha$, then the value of $\int_{4\pi-2}^{4\pi}\dfrac{\sin (t/2)}{4\pi+2-t}dt=$
• A. $-\alpha$
• B. $2\alpha$
• C. $4\pi-2\alpha$
• D. $\alpha$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
$\displaystyle\int \dfrac{x^2}{\sqrt{1-x}}dx$ is equal to?

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value of $\displaystyle \int { { e }^{ 2x } } \left( \frac { 1 }{ x } -\frac { 1 }{ 2{ x }^{ 2 } } \right) dx$ is
• A. $\displaystyle \frac { { e }^{ 2x } }{ 2 } +c$
• B. $\displaystyle \frac { { e }^{ 2x } }{ 3x } +c$
• C. $\displaystyle \frac { { e }^{ 2x } }{ x } +c$
• D. $\displaystyle \frac { { e }^{ 2x } }{ 2x } +c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
The value of $\int {\dfrac{{dx}}{{\sin x.\sin \left( {x + \alpha } \right)}}}$ is equal to

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$