What is the integral of 2^{x^2+1}*x ?

The integral of 2^{x^2+1}*x is (2^{x^2})/(ln(2))+C

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integral of 2^{x^2+1}*x

\int 2^{x^{2} + 1} \cdot x d x

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

Solution steps

\int 2^{x^{2} + 1} x d x

Apply u-substitution

: \int 2^{u} d u

= \int 2^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{2 ^{u}}{ln ( 2 )}

Substitute back

u = x^{2}

= \frac{2 ^{x^{2}}}{ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{x^{2}}}{ln ( 2 )} + C

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What is the integral of 2^{x^2+1}*x ?
The integral of 2^{x^2+1}*x is (2^{x^2})/(ln(2))+C