Mathematics

# $\int \frac{e^{x}(x-1)(x-1nx)}{x^{2}}dx$ is equal to

$e^{x}(\frac{x-1n x}{x})+c$

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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 Medium
Evaluate the given integral.
$\displaystyle\int { \cfrac { x }{ 4+{ x }^{ 4 } } } dx$
• A. $\cfrac { 1 }{ 4 } \tan ^{ -1 }{ { x }^{ 2 } } +C$
• B. $\cfrac { 1 }{ 2 } \tan ^{ -1 }{ \cfrac { { x }^{ 2 } }{ 2 } }$
• C. None of these
• D. $\cfrac { 1 }{ 4 } \tan ^{ -1 }{ \cfrac { { x }^{ 2 } }{ 2 } }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Solve
$\int \sqrt{\dfrac{a-x}{x-b}} dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integral:
$\displaystyle\int^2_1\dfrac{dx}{x(1+log x)^2}$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Evaluate : $\displaystyle\int^a_{-a}\sqrt{\dfrac{a-x}{a+x}}dx$
• A. $\dfrac{a\pi}{2}$
• B. $2a\pi$
• C. None of these
• D. $a\pi$

Let $T=\int_0^{\ln2}\dfrac{2e^{3x}+ 3e^{2x}-6e^x}{6(e^{3x}+e^{2x}-e^x+1)}dx,$ then $e^T=\frac{p}{q}$ where p and q are coprime to each other, then the value of $p+ q$ is