Mathematics

# If $\int {{{1 - 5{{\sin }^2}x} \over {{{\cos }^5}x{{\sin }^2}x}}} dx = {{f\left( x \right)} \over {{{\cos }^5}x}} + C$ , then $f\left( x \right)$ is

$- \cot x$

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

#### Realted Questions

Q1 Single Correct Medium
The value of $\int log x dx$ is
• A. $x^2 log x + c$
• B. $e^x log x + c$
• C. $(x + 1) log x + c$
• D. $\displaystyle x log \left ( \frac{x}{e} \right ) + c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Value of the integral $\displaystyle \int { \cfrac { x^{ 2 }+5x-1 }{ \sqrt { x } } } dx$ is
• A. $\cfrac { 2 }{ 5 } { x }^{ 5/2 }+\cfrac { 2 }{ 3 } 5{ x }^{ 1/2 }-2{ x }^{ 1/2 }+C$
• B. $\cfrac { 3 }{ 5 } { x }^{ 5/2 }+\cfrac { 2 }{ 3 } 5{ x }^{ 1/2 }-2{ x }^{ 1/2 }+C$
• C. $\cfrac { 2 }{ 5 } { x }^{ 5/2 }+\cfrac { 2 }{ 3 } 5{ x }^{ 1/2 }-2{ x }^{ 1/2 }$
• D. $\cfrac { 2 }{ 5 } { x }^{ 5/2 }+\cfrac { 2 }{ 3 } 5{ x }^{ 3/2 }-2{ x }^{ 1/2 }+C$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Find the partial fraction
$\dfrac { 2x+1 }{ \left( 3x+2 \right) \left( 4{ x }^{ 2 }+5x+6 \right) }$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Evaluate: $\displaystyle \int x^{x}(1 + \log x)dx$
• A. $x^{-x} + x$
• B. $x \log x + x$
• C. $\log x + x$
• D. $x^{x} + C$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Medium
$\int { x\tan ^{ 2 }{ x } } dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020