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Popular >

integral of (2x^3)

Solution

\int (2 x^{3}) d x

Solution

\frac{x ^{4}}{2} + C

Solution steps

\int 2 x^{3} d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{4}}{4}

= 2 \cdot \frac{x ^{4}}{4}

Simplify

2 \cdot \frac{x ^{4}}{4} : \frac{x ^{4}}{2}

= \frac{x ^{4}}{2}

Add a constant to the solution

= \frac{x ^{4}}{2} + C

Popular Examples

y^{^{'}} + 2 y = 5

tangent of (3x)/((2-3x)^3),\at x=2 tangent of

\frac{3 x}{( 2 - 3 x ) ^{3}}, at x = 2

integral from 1 to 3 of 3x^2

\int_{1}^{3} 3 x^{2} d x

xy^'+3y=((2e^{-4x}))/(x^2)

x y^{^{'}} + 3 y = \frac{( 2 e ^{- 4 x} )}{x ^{2}}

derivative of y(1+e^x)

\frac{d}{d x} (y (1 + e^{x}))

Frequently Asked Questions (FAQ)

What is the integral of (2x^3) ?
The integral of (2x^3) is (x^4)/2+C