Evaluate the integral : ∫e2In(x2+1)dx

∫e2In(x2+1)dx= ∫eIn(x2+12)2dx = ∫x2+122dx = ∫x4+2x2+1dx =15x5+23x3+x+C

Evaluate the integral : ∫e2In(x2+1)dx

∫e2In(x2+1)dx= ∫eIn(x2+12)2dx = ∫x2+122dx = ∫x4+2x2+1dx =15x5+23x3+x+C

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Evaluate the integral : $\int e^{2 I n (x^{2} + 1)} d x$

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$\frac{1}{5} x^{5} + \frac{3}{2} x^{3} + x + C$

$5 x^{5} + 3 x^{3} + x + C$

$\frac{1}{5} x^{5} + \frac{2}{3} x^{3} + x + C$

$2 x + C$

answer is C.

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Detailed Solution

$\int e^{2 I n (x^{2} + 1)} d x = \int {e^{I n (x^{2} + 1^{2})}}^{2} d x = \int {(x^{2} + 1^{2})}^{2} d x = \int (x^{4} + 2 x^{2} + 1) d x = \frac{1}{5} x^{5} + \frac{2}{3} x^{3} + x + C$

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Evaluate the integral : $\int e^{2 I n (x^{2} + 1)} d x$