What is the integral of 2t*e^t ?

The integral of 2t*e^t is 2(e^tt-e^t)+C

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integral of 2t*e^t

\int 2 t \cdot e^{t} d t

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

Solution steps

\int 2 t e^{t} d t

Take the constant out:

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

= 2 \cdot \int t e^{t} d t

Apply Integration By Parts

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

= 2 (e^{t} t - \int e^{t} d t)

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

= 2 (e^{t} t - e^{t})

Add a constant to the solution

= 2 (e^{t} t - e^{t}) + C

y = x^{2} - 1.521, y = - x^{2} + 1.521

x \to 0 - lim (2^{\frac{1}{x}} + 2)

\frac{e ^{- s}}{s}

(1 + e^{x}) y \frac{d y}{d x} = e^{y}

8 x \frac{d y}{d x} = 2 x e^{x} - 8 y + 6 x^{2}