Mathematics

# Evaluate:$\displaystyle\int \dfrac{\sin^3xdx}{(\cos^4x+3\cos^2x+1)\tan^{-1}(\sec x+\cos x)}$.

##### SOLUTION

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
Evaluate:
$\displaystyle \int\limits_2^0 {\dfrac{1}{{\sqrt {4 - x^2} }}} dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int { \frac { { e }^{ \log { \tan { x } } } }{ 3\tan ^{ 2 }{ x+1 } } dx } =$
• A. $\dfrac {1}{4}\log |3\sin^{2}x+\cos^{2}x|+c$
• B. $\log |3\tan^{2}x+1|+c$
• C. $\dfrac {1}{2}\log |3\sin^{2}x+\cos^{2}x|+c$
• D. $\log |3\sin^{2}x+\cos^{2}x|+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\int {\frac{{dx}}{{\left( {4 + 3{x^2}} \right)\sqrt {3 - 4{x^2}} }} = }$
• A. $\frac{1}{5}{\tan ^{ - 1}}\frac{{2x}}{{\sqrt {3 - 4{x^2}} }} + c$
• B. $\frac{1}{{10}}{\tan ^{ - 1}}\frac{{5x}}{{2\sqrt {3 - 4{x^2}} }} + c$
• C. $\frac{1}{5}{\tan ^{ - 1}}\frac{{5x}}{{2\sqrt {3 - 4{x^2}} }} + c$
• D. $\frac{1}{{10}}{\tan ^{ - 1}}\frac{{5x}}{{\sqrt {3 - 4{x^2}} }} + c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve:
$\int\limits_0^1 {{{\tan }^{ - 1}}\left( {\dfrac{{2x}}{{1 - {x^2}}}} \right)dx}$

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