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

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

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integral of x^2e^{5x}

\int x^{2} 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

8 e^{- x} + e^{3 x}

\int - 2 tan (t) d t

\int tan^{5} (θ) sec^{3} (θ) d θ

\frac{\partial}{\partial x} (x^{3} z + z^{3} x - 2 yz)

f (x) = x^{2} x^{3} + 1, at x = 1

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