What is the integral of e^x*7x ?

The integral of e^x*7x is 7(e^xx-e^x)+C

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integral of e^x*7x

\int e^{x} \cdot 7 x d x

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

Solution steps

\int e^{x} \cdot 7 x d x

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

(u^{2} + u) d x + u^{2} (x d u + u d x) = 0

x \to 4 lim (e^{x} + 4 x)

\int 3 2 x d x

\frac{\partial}{\partial x} (7 x sin (5 x^{2} y))

\int x x x + 1 d x