What is the integral of 17te^t ?

The integral of 17te^t is 17(e^tt-e^t)+C

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integral of 17te^t

\int 17 t e^{t} d t

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

Solution steps

\int 17 t e^{t} d t

Take the constant out:

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

= 17 \cdot \int t e^{t} d t

Apply Integration By Parts

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

= 17 (e^{t} t - \int e^{t} d t)

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

= 17 (e^{t} t - e^{t})

Add a constant to the solution

= 17 (e^{t} t - e^{t}) + C

\frac{d}{d x} (\frac{x ^{4}}{8} + \frac{1}{4 x ^{2}})

\int \frac{3 x}{( x + 1 ) ( x - 2 )} d x

y^{^{''}} + 4 y^{^{'}} + 4 y = x e^{- 2 x}

n \to \infty lim (\frac{1}{5})

y^{^{'}} = \frac{2 y + x}{x}