What is the integral from 0 to ln(5) of 4(5-xe^x) ?

The integral from 0 to ln(5) of 4(5-xe^x) is 16

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integral from 0 to ln(5) of 4(5-xe^x)

\int_{0}^{l n (5)} 4 (5 - x e^{x}) d x

16

Solution steps

\int_{0}^{l n (5)} 4 (5 - x e^{x}) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{l n (5)} 5 - x e^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 4 (\int_{0}^{l n (5)} 5 d x - \int_{0}^{l n (5)} x e^{x} d x)

\int_{0}^{l n (5)} 5 d x = 5 ln (5)

\int_{0}^{l n (5)} x e^{x} d x = 5 ln (5) - 4

= 4 (5 ln (5) - (5 ln (5) - 4))

Simplify

= 16

x \to - \infty lim (\frac{4}{x})

\int (\frac{sin ( x )}{x}) d x

f (x) = x^{7} + x^{5} + x^{3} + x + 1

(3.3) (4.5)

\int_{0}^{\frac{π}{3}} cos^{3} (3 x) d x

What is the integral from 0 to ln(5) of 4(5-xe^x) ?
The integral from 0 to ln(5) of 4(5-xe^x) is 16