JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q74

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MathematicsSingle correct+4 / -1Question 74 of 90

The integral $\displaystyle\int\frac{dx}{x^2(x^4+1)^{3/4}}$ equals :

\left(\dfrac{x^4+1}{x^4}\right)^{\frac14}+c

(x^4+1)^{\frac14}+c

-(x^4+1)^{\frac14}+c

-\left(\dfrac{x^4+1}{x^4}\right)^{\frac14}+c

Answer and worked solution

Official answer: D

Write the integrand as $x^{-5}(1+x^{-4})^{-3/4}$ and put $t=1+x^{-4}$ , $dt=-4x^{-5}dx$ :
$-\frac14\int t^{-3/4}dt=-t^{1/4}=-\left(\frac{x^4+1}{x^4}\right)^{1/4}+c.$

Topics:Substitution

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JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 74