What is the integral of xsqrt(16x^6) ?

The integral of xsqrt(16x^6) is (4x^5)/5+C

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integral of xsqrt(16x^6)

\int x 16 x^{6} d x

\frac{4 x ^{5}}{5} + C

Solution steps

\int x 16 x^{6} d x

Simplify

x 16 x^{6} : 4 x^{4}

= \int 4 x^{4} d x

Take the constant out:

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

= 4 \cdot \int x^{4} d x

Apply the Power Rule

: \frac{x ^{5}}{5}

= 4 \cdot \frac{x ^{5}}{5}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 x ^{5}}{5}

Add a constant to the solution

= \frac{4 x ^{5}}{5} + C

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What is the integral of xsqrt(16x^6) ?
The integral of xsqrt(16x^6) is (4x^5)/5+C