What is the integral of 6te^t ?

The integral of 6te^t is 6(e^tt-e^t)+C

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integral of 6te^t

\int 6 t e^{t} d t

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

Solution steps

\int 6 t e^{t} d t

Take the constant out:

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

= 6 \cdot \int t e^{t} d t

Apply Integration By Parts

= 6 (e^{t} t - \int e^{t} d t)

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

= 6 (e^{t} t - e^{t})

Add a constant to the solution

= 6 (e^{t} t - e^{t}) + C

y^{^{''}} + 4 y^{^{'}} + 40 y = 30 cos (8 t)

\int_{- 3}^{- 3} x^{2} d x

\int \frac{6 x ^{5}}{( x ^{6} + 1 ) ^{2}} d x

\frac{d}{d x} (\frac{e ^{x}}{x ^{n}})

t \frac{d x}{d t} = x - 2 t