What is the integral of x3^{x+1} ?

The integral of x3^{x+1} is (3^{x+1}x)/(ln(3))-1/(ln^2(3))*3^{1+x}+C

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integral of x3^{x+1}

\int x 3^{x + 1} d x

\frac{3 ^{x + 1} x}{ln ( 3 )} - \frac{1}{ln ^{2} ( 3 )} \cdot 3^{1 + x} + C

Solution steps

\int x \cdot 3^{x + 1} d x

Apply Integration By Parts

: \frac{3 ^{x + 1} x}{ln ( 3 )} - \int \frac{3 ^{x + 1}}{ln ( 3 )} d x

= \frac{3 ^{x + 1} x}{ln ( 3 )} - \int \frac{3 ^{x + 1}}{ln ( 3 )} d x

\int \frac{3 ^{x + 1}}{ln ( 3 )} d x = \frac{1}{ln ^{2} ( 3 )} \cdot 3^{1 + x}

= \frac{3 ^{x + 1} x}{ln ( 3 )} - \frac{1}{ln ^{2} ( 3 )} \cdot 3^{1 + x}

Add a constant to the solution

= \frac{3 ^{x + 1} x}{ln ( 3 )} - \frac{1}{ln ^{2} ( 3 )} \cdot 3^{1 + x} + C

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What is the integral of x3^{x+1} ?
The integral of x3^{x+1} is (3^{x+1}x)/(ln(3))-1/(ln^2(3))*3^{1+x}+C