Mathematics

# Prove that$\displaystyle \int \dfrac {x^{2}}{x^{6}+1}dx$

##### SOLUTION
We have,
$\begin{array}{l} \int { \dfrac { { { x^{ 2 } } } }{ { { x^{ 6 } }+1 } } } dx \\ put\, \, \, { x^{ 3 } }=t\, \, \, 3{ x^{ 2 } }dx=dt \\ =\int { \dfrac { { \dfrac { { dt } }{ 3 } } }{ { { t^{ 2 } }+1 } } } \\ =\dfrac { 1 }{ 3 } { \tan ^{ -1 } }t+c \\ =\dfrac { 1 }{ 3 } { \tan ^{ -1 } }{ x^{ 3 } }+c \end{array}$

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

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Find  $\int { \dfrac { ({ x }^{ 2 }+1)({ { x }^{ 2 } }+2) }{ ({ { x }^{ 2 } }+3)({ { x }^{ 2 } }+4) } dx }$

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