What is the integral from 4 to 7 of xe^{7x} ?

The integral from 4 to 7 of xe^{7x} is (48e^{49}-27e^{28})/(49)

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integral from 4 to 7 of xe^{7x}

\int_{4}^{7} x e^{7 x} d x

\frac{48 e ^{49} - 27 e ^{28}}{49}

Decimal

1.86842 E 21

Solution steps

\int_{4}^{7} x e^{7 x} d x

Apply u-substitution

= \int_{28}^{49} \frac{e ^{u} u}{49} d u

Take the constant out:

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

= \frac{1}{49} \cdot \int_{28}^{49} e^{u} u d u

Apply Integration By Parts

= \frac{1}{49} [e^{u} u - \int e^{u} d u]_{28}^{49}

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

= \frac{1}{49} [e^{u} u - e^{u}]_{28}^{49}

Compute the boundaries:

48 e^{49} - 27 e^{28}

= \frac{1}{49} (48 e^{49} - 27 e^{28})

Simplify

= \frac{48 e ^{49} - 27 e ^{28}}{49}

What is the integral from 4 to 7 of xe^{7x} ?
The integral from 4 to 7 of xe^{7x} is (48e^{49}-27e^{28})/(49)