Mathematics

# $\displaystyle\int { \dfrac { { 3x }^{ 13 }+{ 2x }^{ 11 } }{ \left( { 2x }^{ 4 }+{ 3x }^{ 2 }+1 \right) ^{ 4 } } }dx$ is equal to

$\dfrac { 1 }{ 6 } \times \dfrac { 1 }{ \left( 2+\frac { 3 }{ { x }^{ 2 } } +\dfrac { 1 }{ { x }^{ 4 } } \right) ^{ 3 } } +c$

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

#### Realted Questions

Q1 Multiple Correct Medium
$\displaystyle \int \frac{dx}{x^{3}\left ( 1 - \displaystyle \frac{1}{2x^{2}} \right )}$ equals
• A. $ln| 2x^{2} - 1| + 2\, ln |x| + C$
• B. $ln| 2x^{2} - 1| - 2\, ln |x| + C$
• C. $ln| 2x^{2} - 1| - ln (x^{2}) - ln2 + C$
• D. $ln \left | 1 - \displaystyle \frac{1}{2x^{2}} \right | + c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integrals:
$\int { \cfrac { { x }^{ 3 }+x+1 }{ { x }^{ 2 }-1 } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int { \sin ^{ 2 }{ \left( 2x+5 \right) } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
If $\displaystyle f\left ( x \right )$ and $\displaystyle g\left ( x \right )$ be continuous functions over the closed interval $\displaystyle \left [ 0, a \right ]$ such that $\displaystyle f\left ( x \right )= f\left ( a-x \right )$ and $\displaystyle g\left ( x \right )+g\left ( a-x \right )= 2.$ Then $\displaystyle \int_{0}^{a}f\left (x \right )\dot g\left (x \right )dx$ is equal to
• A. $\displaystyle \int_{0}^{a}g\left ( x \right )dx$
• B. $\displaystyle 2a$
• C. none of these
• D. $\displaystyle \int_{0}^{a}f\left ( x \right )dx$

$\displaystyle \int_0^{2\pi}\cos^5x\,\,dx$