JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q74

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MathematicsSingle correct+4 / -1Question 74 of 90

The integral $\displaystyle\int\left(1+x-\frac1x\right)e^{x+\frac1x}\,dx$ is equal to :

(x+1)\,e^{x+\frac1x}+c

-x\,e^{x+\frac1x}+c

(x-1)\,e^{x+\frac1x}+c

x\,e^{x+\frac1x}+c

Answer and worked solution

Official answer: D

$\frac{d}{dx}\left(xe^{x+\frac1x}\right)=e^{x+\frac1x}\left(1+x\left(1-\frac1{x^2}\right)\right)=\left(1+x-\frac1x\right)e^{x+\frac1x}.$
So the integral is $xe^{x+\frac1x}+c$ .

Topics:Integration by parts Standard integrals

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JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 74