What is the integral from 2 to 4 of (x^2+2)^3x ?

The integral from 2 to 4 of (x^2+2)^3x is 12960

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integral from 2 to 4 of (x^2+2)^3x

\int_{2}^{4} (x^{2} + 2)^{3} x d x

12960

Solution steps

\int_{2}^{4} (x^{2} + 2)^{3} x d x

Apply u-substitution

: \int_{6}^{18} \frac{u ^{3}}{2} d u

= \int_{6}^{18} \frac{u ^{3}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{6}^{18} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{6}^{18}

= \frac{1}{2} [\frac{u ^{4}}{4}]_{6}^{18}

Compute the boundaries:

25920

= \frac{1}{2} \cdot 25920

Simplify

= 12960

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\frac{\partial}{\partial y} (ln (x + \frac{y}{2 x}))

\int_{0}^{1} \frac{1}{x ^{\frac{1}{2}}} d x

What is the integral from 2 to 4 of (x^2+2)^3x ?
The integral from 2 to 4 of (x^2+2)^3x is 12960