What is the integral of 4te^t ?

The integral of 4te^t is 4(e^tt-e^t)+C

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integral of 4te^t

\int 4 t e^{t} d t

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

Solution steps

\int 4 t e^{t} d t

Take the constant out:

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

= 4 \cdot \int t e^{t} d t

Apply Integration By Parts

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

= 4 (e^{t} t - \int e^{t} d t)

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

= 4 (e^{t} t - e^{t})

Add a constant to the solution

= 4 (e^{t} t - e^{t}) + C

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\frac{d}{d x} (\frac{c ^{3} - x ^{3}}{c ^{3} + x ^{3}})