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Popular >

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

: \frac{x ^{6}}{6}

= 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

Popular Examples

integral of (sqrt(1+x^2))

\int (1 + x^{2}) d x

f(x)=3xarccos(x)

f (x) = 3 x arccos (x)

integral of 1/1

\int \frac{1}{1} d x

limit as x approaches infinity of 0.5

x \to \infty lim (0.5)

derivative of x(x-5^2)

\frac{d}{d x} (x (x - 5)^{2})

Frequently Asked Questions (FAQ)

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