What is the integral of x^2*e^{5x} ?

The integral of x^2*e^{5x} is 1/5 e^{5x}x^2-2/125 (5e^{5x}x-e^{5x})+C

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integral of x^2*e^{5x}

\int x^{2} \cdot e^{5 x} d x

\frac{1}{5} e^{5 x} x^{2} - \frac{2}{125} (5 e^{5 x} x - e^{5 x}) + C

Solution steps

\int x^{2} e^{5 x} d x

Apply Integration By Parts

: \frac{1}{5} e^{5 x} x^{2} - \int \frac{2}{5} e^{5 x} x d x

= \frac{1}{5} e^{5 x} x^{2} - \int \frac{2}{5} e^{5 x} x d x

\int \frac{2}{5} e^{5 x} x d x = \frac{2}{125} (5 e^{5 x} x - e^{5 x})

= \frac{1}{5} e^{5 x} x^{2} - \frac{2}{125} (5 e^{5 x} x - e^{5 x})

Add a constant to the solution

= \frac{1}{5} e^{5 x} x^{2} - \frac{2}{125} (5 e^{5 x} x - e^{5 x}) + C

n = - 1 \sum \infty (\frac{1}{2})^{n}

\int_{- \infty}^{0} \frac{1}{7 - 10 x} d x

\frac{d}{d x} (2 x^{2} + 3 x - 5)

\int \frac{x ^{3}}{3} (\frac{1}{x}) d x

\int \frac{2 x ^{5}}{3 x ^{2} + 4} d x

What is the integral of x^2*e^{5x} ?
The integral of x^2*e^{5x} is 1/5 e^{5x}x^2-2/125 (5e^{5x}x-e^{5x})+C