What is the integral of 7te^t ?

The integral of 7te^t is 7(e^tt-e^t)+C

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integral of 7te^t

\int 7 t e^{t} d t

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

Solution steps

\int 7 t e^{t} d t

Take the constant out:

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

= 7 \cdot \int t e^{t} d t

Apply Integration By Parts

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

= 7 (e^{t} t - \int e^{t} d t)

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

= 7 (e^{t} t - e^{t})

Add a constant to the solution

= 7 (e^{t} t - e^{t}) + C

\frac{( 2 + x ) d y}{d x} = 3 y

x \to a lim (x)

x \to 7 lim (8 x - 3)

\frac{\partial}{\partial u} (tan (u v^{3}))

(x y^{2} + x^{3}) d x + (y^{3} + x^{2} y) d y = 0