What is the integral from 0 to 1 of 4x+e^{3x} ?

The integral from 0 to 1 of 4x+e^{3x} is 2+(e^3-1)/3

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integral from 0 to 1 of 4x+e^{3x}

\int_{0}^{1} 4 x + e^{3 x} d x

2 + \frac{e ^{3} - 1}{3}

Decimal

8.36184 \dots

Solution steps

\int_{0}^{1} 4 x + e^{3 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

= \int_{0}^{1} 4 x d x + \int_{0}^{1} e^{3 x} d x

\int_{0}^{1} 4 x d x = 2

\int_{0}^{1} e^{3 x} d x = \frac{e ^{3} - 1}{3}

= 2 + \frac{e ^{3} - 1}{3}

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What is the integral from 0 to 1 of 4x+e^{3x} ?
The integral from 0 to 1 of 4x+e^{3x} is 2+(e^3-1)/3