What is the integral of 20te^t ?

The integral of 20te^t is 20(e^tt-e^t)+C

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integral of 20te^t

\int 20 t e^{t} d t

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

Solution steps

\int 20 t e^{t} d t

Take the constant out:

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

= 20 \cdot \int t e^{t} d t

Apply Integration By Parts

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

= 20 (e^{t} t - \int e^{t} d t)

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

= 20 (e^{t} t - e^{t})

Add a constant to the solution

= 20 (e^{t} t - e^{t}) + C

f (x) = 4 x^{2} + 7, (- 3, 43)

(- 4, - 6), (4, - 2)

f (x) = \frac{- 4 x}{x ^{2} + 1}, (1, - 2)

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

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