What is the integral from 1 to 25 of 5xe^{2x} ?

The integral from 1 to 25 of 5xe^{2x} is (5(49e^{50}-e^2))/4

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integral from 1 to 25 of 5xe^{2x}

\int_{1}^{25} 5 x e^{2 x} d x

\frac{5 ( 49 e ^{50} - e ^{2} )}{4}

Decimal

3.17563 E 23

Solution steps

\int_{1}^{25} 5 x e^{2 x} d x

Take the constant out:

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

= 5 \cdot \int_{1}^{25} x e^{2 x} d x

Apply u-substitution

= 5 \cdot \int_{2}^{50} \frac{e ^{u} u}{4} d u

Take the constant out:

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

= 5 \cdot \frac{1}{4} \cdot \int_{2}^{50} e^{u} u d u

Apply Integration By Parts

= 5 \cdot \frac{1}{4} [e^{u} u - \int e^{u} d u]_{2}^{50}

\int e^{u} d u = e^{u}

= 5 \cdot \frac{1}{4} [e^{u} u - e^{u}]_{2}^{50}

Simplify

5 \cdot \frac{1}{4} [e^{u} u - e^{u}]_{2}^{50} : \frac{5}{4} [e^{u} u - e^{u}]_{2}^{50}

= \frac{5}{4} [e^{u} u - e^{u}]_{2}^{50}

Compute the boundaries:

49 e^{50} - e^{2}

= \frac{5}{4} (49 e^{50} - e^{2})

Simplify

= \frac{5 ( 49 e ^{50} - e ^{2} )}{4}

What is the integral from 1 to 25 of 5xe^{2x} ?
The integral from 1 to 25 of 5xe^{2x} is (5(49e^{50}-e^2))/4