What is the integral of 3^xx ?

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

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integral of 3^xx

\int 3^{x} x d x

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

Solution steps

\int 3^{x} x d x

Apply Integration By Parts

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

= \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

f (0) = \frac{x}{x ^{2} + 4}

\int_{0}^{1} (\frac{x ^{3} + 1}{x + 1}) d x

\frac{\partial}{\partial x} (x^{\frac{1}{2}} + y^{\frac{1}{2}})

20 + x - x^{2}, x^{2} - 5 x, [4, 8]

e^{c o s^{2} (π t - 11)}

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