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Popular >

integral of 15x^2

Solution

\int 15 x^{2} d x

Solution

5 x^{3} + C

Solution steps

\int 15 x^{2} d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= 15 \cdot \frac{x ^{3}}{3}

Simplify

15 \cdot \frac{x ^{3}}{3} : 5 x^{3}

= 5 x^{3}

Add a constant to the solution

= 5 x^{3} + C

Popular Examples

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\int sec^{2} (3 x) e^{t a n (3 x) - 2} d x

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\int \frac{1}{4 + u ^{2}} d u

xy^'+y=e^x,y(1)=2

x y^{^{'}} + y = e^{x}, y (1) = 2

derivative of sqrt(cos^2(x-sin^2(x)))

\frac{d}{d x} (cos^{2} (x) - sin^{2} (x))

derivative of arctan((x+1/(x-1)))

\frac{d}{d x} (arctan (\frac{x + 1}{x - 1}))

Frequently Asked Questions (FAQ)

What is the integral of 15x^2 ?
The integral of 15x^2 is 5x^3+C