JEE Mains 2016 Mathematics 33

Calculus Level 4

$\large \int \frac {2x^{12}+5x^9}{(x^5+ x^3+1)^3} \ dx$

What is the above integral equal to?

Notation: $C$ denotes the constant of integration .

-\frac { { x }^{ 10 } }{ { \left( { x }^{ 5 }+{ x }^{ 3 }+1 \right) }^{ 2 } } +C

\frac { { -x }^{ 5 } }{ { \left( { x }^{ 5 }+{ x }^{ 3 }+1 \right) }^{ 2 } } +C

\frac { { x }^{ 10 } }{ { 2\left( { x }^{ 5 }+{ x }^{ 3 }+1 \right) }^{ 2 } } +C

\frac { { x }^{ 5 } }{ { 2\left( { x }^{ 5 }+{ x }^{ 3 }+1 \right) }^{ 2 } } +C

1 solution

Raghu Raman Ravi
Sep 16, 2017

Just a hint. Divide numerator and denominator by x^15, and substitute the denominator as t^3.