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Popular Calculus >

integral of 5x^33x^2

Solution

\int 5 x^{3} 3 x^{2} d x

Solution

\frac{5 x ^{6}}{2} + C

Solution steps

\int 5 x^{3} \cdot 3 x^{2} d x

Take the constant out:

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

= 5 \cdot 3 \cdot \int x^{3} x^{2} d x

Simplify

= 15 \cdot \int x^{3} x^{2} d x

Simplify

x^{3} x^{2} : x^{5}

= 15 \cdot \int x^{5} d x

Apply the Power Rule

= 15 \cdot \frac{x ^{6}}{6}

Simplify

15 \cdot \frac{x ^{6}}{6} : \frac{5 x ^{6}}{2}

= \frac{5 x ^{6}}{2}

Add a constant to the solution

= \frac{5 x ^{6}}{2} + C

Graph

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(\partial)/(\partial y)(-1/(x-y))

Frequently Asked Questions (FAQ)

What is the integral of 5x^33x^2 ?
The integral of 5x^33x^2 is (5x^6)/2+C