Mathematics

# $\displaystyle \int \dfrac { dx }{ { \left( 1+x \right) }^{ 5 }\sqrt { { { x }^{ 2 } }+2x } } =\dfrac { -1 }{ 8 } \left( 3\theta -2\sin { 2\theta +\dfrac { \sin { 4\theta } }{ 4 } } \right) +c$ where

$\theta =\sin ^{ -1 }{ \left( x+1 \right) }$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Single Correct Hard
The value of $\displaystyle \int ^{\tan x}_{1/e}\displaystyle \frac{t\, dt}{1+t^{2}}+\displaystyle \int ^{\cot x}_{1/e}\displaystyle \frac{dt}{t\left ( 1+t^{2} \right )}$ is
• A. $\displaystyle \frac{1}{2+tan^{2}x}$
• B. $\pi /4$
• C. $\displaystyle \frac{2}{\pi }\displaystyle \int ^{1}_{-1}\displaystyle \frac{dt}{1+t^{2}}$
• D. $1$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral:
$\displaystyle\int{{a}^{\log_{a}{x}}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle f\left ( 8-t \right )=f\left ( t \right )$ and $\displaystyle \int_{0}^{4}f\left ( a \right )da=8,$ then $\displaystyle \int_{0}^{8}f\left ( y \right )dy$ is
• A. 4
• B. 8
• C. 32
• D. 16

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate : $\displaystyle \int ^x_{-x} (\cos ax - \sin bx)^2 dx$.

$\displaystyle _{0}^{5}\int \dfrac{4\sqrt{x+4}}{4\sqrt{x+4}+4\sqrt{9-x}}$