What is the integral of 7xe^x ?

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

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integral of 7xe^x

\int 7 x e^{x} d x

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

Solution steps

\int 7 x e^{x} d x

Take the constant out:

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

= 7 \cdot \int x e^{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

y = x, y = x

4 cos (x^{2})

x \to 3 lim (\frac{1}{x ^{2} - 9})

t \to π lim (tan (\frac{t}{6}))

\int_{1}^{5} \frac{x ^{2} + 1}{6 x - x ^{2}} d x