Mathematics

# Evaluate the following integration w.r.t. $x$ $x^{2}\int (1-\dfrac {2}{x})^{2}dx$

$\left[\dfrac{x^3}{3}+4x+\dfrac{4}{x^2}\right]+c$

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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 Hard
$\int { \dfrac { { \left( x+\sqrt { 1+{ x }^{ 2 } } \right) }^{ 15 } }{ \sqrt { 1+{ x }^{ 2 } } } } dx=$
• A. $\dfrac { { \left( x+\sqrt { 1+{ x }^{ 2 } } \right) }^{ 15 } }{ 15 } +C$
• B. $\dfrac { { \left( x+\sqrt { 1+{ x }^{ 2 } } \right) }^{ 15 } }{ 30x } +C$
• C. $\dfrac { { \left( x+\sqrt { 1+{ x }^{ 2 } } \right) }^{ 15 } }{ 15x } +C$
• D. $\dfrac { { \left( x+\sqrt { 1+{ x }^{ 2 } } \right) }^{ 15 } }{ 30 } +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If f(x) $If(x)=\begin{cases} \frac { { 36 }^{ x }-{ 9 }^{ x }-4^{ x }+1 }{ \sqrt { 2 } -\sqrt { 1+cosx } } ,x\neq 0 \\ \quad \quad \quad \quad k\quad \quad \quad \quad \quad \quad \quad \quad \quad ,x=0 \end{cases}$ is continuous at x=0, then k equals
• A. $16\sqrt { 2 } log\quad 2\quad log\quad 3$
• B. $16\sqrt { 2 } In 6$
• C. None of these
• D. $16\sqrt { 2 }$ In $2$ In $3$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate the following function with respect to x:
$\int { \cfrac { 1 }{ \left( { x }^{ 2 }-1 \right) } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following : $\displaystyle\int \dfrac{1}{4x^{2}-3}.dx$

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. $\dfrac{2}{5}(\sqrt{17}+\sqrt{2})$