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

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

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integral of e^{5x}x^2

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

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

\int t^{2} e^{- t} d t

x \to 2 lim (\frac{1}{x ^{2} - 1})

y = \frac{1}{8 x ^{2}}, y = x, y = \frac{x}{8}

\frac{d}{d x} (x sec (y))

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