What is the integral of 3^xx^2 ?

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

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integral of 3^xx^2

\int 3^{x} x^{2} d x

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

Solution steps

\int 3^{x} x^{2} d x

Apply Integration By Parts

: \frac{3 ^{x} x ^{2}}{ln ( 3 )} - \int \frac{2 \cdot 3 ^{x} x}{ln ( 3 )} d x

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

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

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

Add a constant to the solution

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

x \to 4 lim (x - 3)

\frac{6}{x ^{6}}

x \to 6 + lim (\frac{∣ x - 6 ∣}{x - 6})

\frac{d}{d E} (E i)

n = 1 \sum \infty \frac{2}{n ^{2} + 4 n + 3}

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