What is the integral from 0 to ln(2) of 4(2-xe^x) ?

The integral from 0 to ln(2) of 4(2-xe^x) is 4

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integral from 0 to ln(2) of 4(2-xe^x)

\int_{0}^{l n (2)} 4 (2 - x e^{x}) d x

4

Solution steps

\int_{0}^{l n (2)} 4 (2 - 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 (2)} 2 - 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 (2)} 2 d x - \int_{0}^{l n (2)} x e^{x} d x)

\int_{0}^{l n (2)} 2 d x = 2 ln (2)

\int_{0}^{l n (2)} x e^{x} d x = 2 ln (2) - 1

= 4 (2 ln (2) - (2 ln (2) - 1))

Simplify

= 4

x^{2} \frac{d ^{2} y}{d x ^{2}} + x \frac{d y}{d x} + y = 0

f (x) = e^{t a n (x)}

\frac{d}{d x} (1 - (x^{2} + y^{2})^{\frac{1}{3}})

\int 4 x - 3 - x^{2} d x

\frac{\partial}{\partial x} (\frac{1}{x yz})

What is the integral from 0 to ln(2) of 4(2-xe^x) ?
The integral from 0 to ln(2) of 4(2-xe^x) is 4