What is the integral of-3xe^x ?

The integral of-3xe^x is -3(e^xx-e^x)+C

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integral of-3xe^x

\int - 3 x e^{x} d x

- 3 (e^{x} x - e^{x}) + C

Solution steps

\int - 3 x e^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 3 \cdot \int x e^{x} d x

Apply Integration By Parts

: e^{x} x - \int e^{x} d x

= - 3 (e^{x} x - \int e^{x} d x)

\int e^{x} d x = e^{x}

= - 3 (e^{x} x - e^{x})

Add a constant to the solution

= - 3 (e^{x} x - e^{x}) + C

\int \frac{3}{x} + x d x

\int_{0}^{27} \frac{5}{x ^{\frac{2}{3}}} d x

y^{^{'}} = 3 x + y, y (0) = 2

\int x^{2} + 5 d x

r \to 0 lim (sin^{2} (r))