What is the integral of x(3^x) ?

The integral of x(3^x) is (3^xx)/(ln(3))-(3^x)/(ln^2(3))+C

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integral of x(3^x)

\int x (3^{x}) d x

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

What is the integral of x(3^x) ?
The integral of x(3^x) is (3^xx)/(ln(3))-(3^x)/(ln^2(3))+C