JEE Main 2015 · 10 Apr · Shift 1 · Mathematics Q74

← JEE Main 2015 · 10 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 74 of 90

The integral $\displaystyle\int\frac{dx}{(x+1)^{\frac34}(x-2)^{\frac54}}$ is equal to :

4\left(\dfrac{x+1}{x-2}\right)^{\frac14}+C

4\left(\dfrac{x-2}{x+1}\right)^{\frac14}+C

-\dfrac43\left(\dfrac{x+1}{x-2}\right)^{\frac14}+C

-\dfrac43\left(\dfrac{x-2}{x+1}\right)^{\frac14}+C

Answer and worked solution

Official answer: C

Write the integrand as $\dfrac1{(x-2)^2}\left(\dfrac{x+1}{x-2}\right)^{-3/4}$ and put $t=\dfrac{x+1}{x-2}$ , $dt=-\dfrac3{(x-2)^2}dx$ :
$-\frac13\int t^{-3/4}dt=-\frac43t^{1/4}=-\frac43\left(\frac{x+1}{x-2}\right)^{1/4}+C.$

Topics:Substitution

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JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 74