Mathematics

# The value of $\displaystyle \int \dfrac {\sin^{6}x+\cos^{6}x}{\sin^{2}x.\cos^{2}x}dx$ equals

$-(\tan x+\cot x)+c$

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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 Hard
$\int { \cfrac { \cos { x } }{ \sqrt { 4-\sin ^{ 2 }{ x } } } } dx=$?
• A. $\sin ^{ -1 }{ \left( \cfrac { x }{ 2 } \right) } +C$
• B. $\sin ^{ -1 }{ \left( \cfrac { 1 }{ 2 } \cos { x } \right) } +C$
• C. $\cfrac { 1 }{ 2 } \sin ^{ -1 }{ \left( 2\sin { x } \right) } +C$
• D. $\sin ^{ -1 }{ \left( \cfrac { 1 }{ 2 } \sin { x } \right) } +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve  $\displaystyle\int {\dfrac{x}{{9 - 4{x^2}}}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integral as limit of sum:
$\displaystyle \int_{a}^{b}x\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Find $\displaystyle \int \sqrt {1 + \cos2x} dx$.

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \int \dfrac{1}{x^2 (x^4 + 1)^{\frac{3}{4}}}dx$ is equal to
• A. $-\dfrac{(1 + x^4)^{\frac{3}{4}}}{x} + C$
• B. $-\dfrac{(1 + x^4)^{\frac{1}{4}}}{2x} + C$
• C. $-\dfrac{(1 + x^4)^{\frac{1}{4}}}{x^2} + C$
• D. $-\dfrac{(- 1 + x^4)^{\frac{1}{2}}}{x} + C$
• E. $-\dfrac{(1 + x^4)^{\frac{1}{4}}}{x} + C$