JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q74

← JEE Main 2016 · 3 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 74 of 90

The integral $\displaystyle\int\frac{2x^{12}+5x^9}{\left(x^5+x^3+1\right)^3}\,dx$ is equal to :

where C is an arbitrary constant.

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

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

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

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

Answer and worked solution

Official answer: B

Divide top and bottom by $x^{15}$ : the integrand is $\dfrac{2x^{-3}+5x^{-6}}{(1+x^{-2}+x^{-5})^3}$ . With $t=1+x^{-2}+x^{-5}$ , $dt=-(2x^{-3}+5x^{-6})dx$ :
$\int-\frac{dt}{t^3}=\frac1{2t^2}=\frac{x^{10}}{2(x^5+x^3+1)^2}+C.$

Topics:Substitution

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 74