Mathematics

# $\displaystyle \int { \dfrac { dx }{ x\sqrt { { x }^{ 6 }+1 } } }$ equals to

$\sec^ {-1}x^ {3}+C$

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

#### Realted Questions

Q1 Subjective Medium
Evaluate:
$\displaystyle \int \dfrac { x ^ { 3 } } { ( x + 1 ) ^ { 2 } } d x$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int { \dfrac { \left( 1+x \right) { e }^{ x } }{ \cot { \left( x{ e }^{ x } \right) } } dx }$ is equal to
• A. $\log { \left| \cos { \left( x{ e }^{ x } \right) } \right| } +C$
• B. $\log { \left| \cot { \left( x{ e }^{ x } \right) } \right| } +C$
• C. $\log { \left| \cos { \left( x{ e }^{ -x } \right) } \right| } +C$
• D. $\log { \left| \sec { \left( x{ e }^{ x } \right) } \right| } +C$
• E. $\log { \left| \sec { \left( x{ e }^{ -x } \right) } \right| } +C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Evaluate : $\displaystyle \int \frac{\left ( 4x+1 \right )\; dx}{x^{2}+3x+2}$
• A. $\displaystyle=2\:log\left | x^{2}+5x+2 \right |-5log\left | \frac{x+1}{x+2} \right |+C$
• B. $\displaystyle=2\:log\left | x^{2}+3x+2 \right |-5log\left | \frac{x+3}{x+2} \right |+C$
• C. $\displaystyle=2\:log\left | x^{2}+3x+2 \right |-5log\left | \frac{x+1}{x+3} \right |+C$
• D. $\displaystyle=2\:log\left | x^{2}+3x+2 \right |-5log\left | \frac{x+1}{x+2} \right |+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Prove that: $\displaystyle\int^1_{-1}(ax^3+bx)dx=0$ .

Find $\int a^{x} \cdot e^{x} dx$.