Mathematics

# $\displaystyle \int \dfrac {\sin x}{\sin 4x}dx$

$\dfrac { 1 }{ 2\sqrt { 2 } } \log { \left| \dfrac { 1+\sqrt { 2\sin { x } } }{ 1-\sqrt { 2\sin { x } } } \right| } +\dfrac { 1 }{ 8 } \log { \left| \dfrac { 1+\sin { x } }{ 1-\sin { x } } \right| +C }$

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

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int\frac{e^{x}}{e^{2x}+5e^{x}+6}dx=$
• A. $\displaystyle \log|\frac{e^{x}+3}{e^{x}+2}|+c$
• B. $\displaystyle \log|\frac{e^{x}-2}{e^{x}-3}|+c$
• C. $\displaystyle \log|\frac{e^{x}-3}{e^{x}-2}|+c$
• D. $\displaystyle \log|\frac{e^{x}+2}{e^{x}+3}|+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
$\displaystyle \int { \sqrt { \sin { x } } }$dx

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Prove that $\displaystyle\int^{\infty}_0\dfrac{x}{(1+x)(1+x^2)}dx=\dfrac{\pi}{4}$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int \dfrac {dx}{\sqrt {x}(x+9)}$ is equal to, $(x > 0)$
• A. $\dfrac {2}{5}\tan^{-1}(\sqrt {x})+c$
• B. $\tan^{-1}(\sqrt {x})+c$
• C. $\tan^{-1}\left(\dfrac {\sqrt {x}}{3}\right)+c$
• D. $\dfrac {2}{3}\tan^{-1}\left(\dfrac {\sqrt {x}}{3}\right)+c$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
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 $\displaystyle f(x)>0 \forall x \in R$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives

1 Verified Answer | Published on 17th 08, 2020