What is the integral from 1 to 3 of (x^2+3)^3x ?

The integral from 1 to 3 of (x^2+3)^3x is 2560

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integral from 1 to 3 of (x^2+3)^3x

\int_{1}^{3} (x^{2} + 3)^{3} x d x

2560

Solution steps

\int_{1}^{3} (x^{2} + 3)^{3} x d x

Apply u-substitution

= \int_{4}^{12} \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_{4}^{12} u^{3} d u

Apply the Power Rule

= \frac{1}{2} [\frac{u ^{4}}{4}]_{4}^{12}

Compute the boundaries:

5120

= \frac{1}{2} \cdot 5120

Simplify

= 2560

What is the integral from 1 to 3 of (x^2+3)^3x ?
The integral from 1 to 3 of (x^2+3)^3x is 2560