Mathematics

# $\displaystyle \int \frac{sin\, 2x}{sin^4\, x\, +\, cos^4\, x}dx$ is equal to

$cot^{-1}\, (cot^2\, x)\, +\, c$

$-cot^{-1}\, (tan^2\, x)\, +\, c$

$tan^{-1}\, (tan^2\, x)\, +\, c$

$-tan^{-1}\, (cos2x\, x)\, +\, c$

Its FREE, you're just one step away

Multiple Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Hard
$\displaystyle \int \frac{\cot^{-1}(e^x)}{e^x} dx$ is equal to:
• A. $\displaystyle \frac{1}{2}\ln (e^{2x}+1)-\displaystyle \frac{\cot^{-1}(e^x)}{(e^x)}+x+c$
• B. $\displaystyle \frac{1}{2}\ln (e^{2x}+1)+\displaystyle \frac{\cot^{-1}(e^x)}{(e^x)}+x+c$
• C. $\displaystyle \frac{1}{2}\ln (e^{2x}+1)+\displaystyle \frac{\cot^{-1}(e^x)}{(e^x)}-x+c$
• D. $\displaystyle \frac{1}{2}\ln (e^{2x}+1)-\displaystyle \frac{\cot^{-1}(e^x)}{(e^x)}-x+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Evaluate: $\displaystyle{\int \dfrac{1}{\sin x + \sec x}}\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium

$\displaystyle \int_{0}^{\infty}\frac{dx}{(x+\sqrt{x^{2}+1})^{5}}=$
• A. 1/24
• B. 1/5
• C. 5/36
• D. 5/24

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $\displaystyle f\left ( x \right )$ is a function of $x$ such that $\displaystyle \frac{1}{\left ( 1 + x \right ) \left ( 1 + x^{2} \right )} = \frac{A}{1 + x} + \frac{f\left ( x \right )}{1 + x^{2}}$ for all $\displaystyle x \: \epsilon \: R$ then $\displaystyle f\left ( x \right )$ is
• A. $\displaystyle \frac{x + 1}{2}$
• B. $\displaystyle 1 - x$
• C. none of these
• D. $\displaystyle \frac{1 - x}{2}$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$