What is the integral of-3te^t ?

The integral of-3te^t is -3(e^tt-e^t)+C

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integral of-3te^t

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int \frac{( 1 - x )}{x ^{2} + 1} d x

\frac{\partial}{\partial x} (x^{y + z})

\int x^{2} ln (2 x - 3) d x

x \to - 1 lim (x^{2} + 5 x + 6)

y^{^{''}} - 7 y^{^{'}} = - 3