Primitive of $f(x)=x \cdot 2^{\ln \left(x^2+1\right)}$ w.r.t. $x$ is

$\frac{2^{\ln \left(x^2+1\right)}}{2\left(x^2+1\right)}+C$

$\frac{\left(\mathrm{x}^2+1\right) 2^{\ln \left\{\mathrm{x}^2+1\right\}}}{\ln 2+1}+\mathrm{C}$

$\frac{\left(x^2+1\right)^{\ln 2}}{2(\ln 2+1)}+C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Medium

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Application +4 | -1

Primitive of

f(x)=x \cdot 2^{\ln \left(x^2+1\right)}

w.r.t.

x

View answer and explanation

Correct option: C

\frac{\left(\mathrm{x}^2+1\right)^{\ln 2+1}}{2(\ln 2+1)}+\mathrm{C}

Option C (

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

) is correct because after substituting

t = x^2 + 1

and integrating, we arrive at the given result.