What is the integral of 3te^t ?

The integral of 3te^t is 3(e^tt-e^t)+C

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integral of 3te^t

\int 3 t e^{t} d t

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

Solution steps

\int 3 t e^{t} d t

Take the constant out:

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

= 3 \cdot \int t e^{t} d t

Apply Integration By Parts

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

= 3 (e^{t} t - \int e^{t} d t)

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

= 3 (e^{t} t - e^{t})

Add a constant to the solution

= 3 (e^{t} t - e^{t}) + C

\int \frac{x ^{2}}{x ^{3} + 3} d x

x \to π - lim ((π - x) csc (x))

\int (sin (x))^{2} d x

\int x^{4} (x^{5} + 1)^{9} d x

\frac{d}{d x} y + 3 y x^{5} = 0