What is the integral from 0 to 1 of (5x+1)e^{5x} ?

The integral from 0 to 1 of (5x+1)e^{5x} is e^5

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integral from 0 to 1 of (5x+1)e^{5x}

\int_{0}^{1} (5 x + 1) e^{5 x} d x

e^{5}

Decimal

148.41315 \dots

Solution steps

\int_{0}^{1} (5 x + 1) e^{5 x} d x

Apply Integration By Parts

= [e^{5 x} x + \frac{1}{5} e^{5 x} - \int e^{5 x} d x]_{0}^{1}

\int e^{5 x} d x = \frac{1}{5} e^{5 x}

= [e^{5 x} x + \frac{1}{5} e^{5 x} - \frac{1}{5} e^{5 x}]_{0}^{1}

Add similar elements:

\frac{1}{5} e^{5 x} - \frac{1}{5} e^{5 x} = 0

= [e^{5 x} x]_{0}^{1}

Compute the boundaries:

e^{5}

= e^{5}

What is the integral from 0 to 1 of (5x+1)e^{5x} ?
The integral from 0 to 1 of (5x+1)e^{5x} is e^5