What is the integral of x^2e^{x/7} ?

The integral of x^2e^{x/7} is 7e^{x/7}x^2-14(7e^{x/7}x-49e^{x/7})+C

Popular >

integral of x^2e^{x/7}

\int x^{2} e^{\frac{x}{7}} d x

7 e^{\frac{x}{7}} x^{2} - 14 (7 e^{\frac{x}{7}} x - 49 e^{\frac{x}{7}}) + C

Solution steps

\int x^{2} e^{\frac{x}{7}} d x

Apply Integration By Parts

: 7 e^{\frac{x}{7}} x^{2} - \int 14 e^{\frac{x}{7}} x d x

= 7 e^{\frac{x}{7}} x^{2} - \int 14 e^{\frac{x}{7}} x d x

\int 14 e^{\frac{x}{7}} x d x = 14 (7 e^{\frac{x}{7}} x - 49 e^{\frac{x}{7}})

= 7 e^{\frac{x}{7}} x^{2} - 14 (7 e^{\frac{x}{7}} x - 49 e^{\frac{x}{7}})

Add a constant to the solution

= 7 e^{\frac{x}{7}} x^{2} - 14 (7 e^{\frac{x}{7}} x - 49 e^{\frac{x}{7}}) + C

\int \frac{1}{1 + 4 x ^{2} + 1} d x

\int \frac{x}{4 9 - x ^{2}} d x

\int \frac{1}{1 + e ^{11 x}} d x

\int \frac{x + 3}{x ^{2} + 2 x + 10} d x

\int (x^{3} - 1) sin (\frac{π}{2} - x) d x

What is the integral of x^2e^{x/7} ?
The integral of x^2e^{x/7} is 7e^{x/7}x^2-14(7e^{x/7}x-49e^{x/7})+C