Mathematics

# Integrate: $f(x)=\dfrac { \sin ^{ 3 }{ x } +\cos ^{ 3 }{ x } }{ \sin ^{ 2 }{ x } \cos ^{ 2 }{ x } }$

##### SOLUTION
$\int \dfrac{\sin^3 x + \cos^3 x}{\sin^2 x \cos^2 x} dx$

$= \int \dfrac{\sin x}{\cos^2 x} dx + \int \dfrac{\cos x}{\sin^2 x} dx$

$= \int \sec x \tan x dx + \int \csc x \cot x dx$

$= \sec x - \csc x + c$ (Ans)

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

#### Realted Questions

Q1 Subjective Medium
Evaluate the following integral:
$\displaystyle\int{{a}^{\log_{a}{x}}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\int { \cfrac { dx }{ (4{ x }^{ 2 }-4x+3) } } =$?
• A. $\cfrac { 1 }{ \sqrt { 2 } } \tan ^{ -1 }{ \left( \cfrac { 2x-1 }{ \sqrt { 2 } } \right) } +C$
• B. $-\cfrac { 1 }{ \sqrt { 2 } } \tan ^{ -1 }{ \left( \cfrac { 2x-1 }{ \sqrt { 2 } } \right) } +C$
• C. none of these
• D. $\cfrac { 1 }{ 2\sqrt { 2 } } \tan ^{ -1 }{ \left( \cfrac { 2x-1 }{ \sqrt { 2 } } \right) } +C$

1 Verified Answer | Published on 17th 09, 2020

Q3 One Word Medium
$\displaystyle \int \frac{e^{x}dx}{\left ( e^{x}-3e^{-x}+2 \right )}= \frac{1}{k}\log \left ( e^{x}-1 \right )\left ( e^{x}+3 \right )^{3}.$ Find the value of $k$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\displaystyle \int { \frac { 1 }{(1-2x) } }dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle\overset{\pi/2}{\underset{0}{\displaystyle\int}}\cos^3xdx =$ ___________.
• A. $\dfrac{8}{3}$
• B. $0$
• C. $1$
• D. $\dfrac{2}{3}$