What is the integral from 0 to 2 of x3^x ?

The integral from 0 to 2 of x3^x is (18ln(3)-8)/(ln^2(3))

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integral from 0 to 2 of x3^x

\int_{0}^{2} x 3^{x} d x

\frac{18 ln ( 3 ) - 8}{ln ^{2} ( 3 )}

Decimal Notation

9.75602 \dots

Solution steps

\int_{0}^{2} x \cdot 3^{x} d x

Apply Integration By Parts

: [\frac{3 ^{x} x}{ln ( 3 )} - \int \frac{3 ^{x}}{ln ( 3 )} d x]_{0}^{2}

= [\frac{3 ^{x} x}{ln ( 3 )} - \int \frac{3 ^{x}}{ln ( 3 )} d x]_{0}^{2}

\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 )}]_{0}^{2}

Compute the boundaries:

\frac{18 ln ( 3 ) - 8}{ln ^{2} ( 3 )}

= \frac{18 ln ( 3 ) - 8}{ln ^{2} ( 3 )}

\int \frac{( x ^{2} + 2 )}{x + 2} d x

\frac{\partial}{\partial x} \frac{( x - y )}{ln ( \frac{x}{y} )}

2 \frac{d ^{2} y}{d x ^{2}} - 20 \frac{d y}{d x} + 48 y = 3 sin (5 x)

\frac{s}{s ^{2} + 2 s + 2}

\int (\frac{y}{2} - tan (x)) y d x

What is the integral from 0 to 2 of x3^x ?
The integral from 0 to 2 of x3^x is (18ln(3)-8)/(ln^2(3))