What is the integral of-te^t ?

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

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integral of-te^t

\int - t e^{t} d t

- e^{t} t + e^{t} + C

Solution steps

\int - t e^{t} d t

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

Simplify

= - e^{t} t + e^{t}

Add a constant to the solution

= - e^{t} t + e^{t} + C

\int \frac{1}{10 - x ^{2}} d x

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

\frac{d ^{2}}{d x ^{2}} ((cos (2 x)) (sin (6 x)))

\int \frac{cos ( x )}{sin ^{12} ( x )} d x

d er i v a t i v e y = e