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Popular >

integral of (4x^3)

Solution

\int (4 x^{3}) d x

Solution

x^{4} + C

Solution steps

\int 4 x^{3} d x

Take the constant out:

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

= 4 \cdot \int x^{3} d x

Apply the Power Rule

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

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

Simplify

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

= x^{4}

Add a constant to the solution

= x^{4} + C

Popular Examples

integral from 1 to sqrt(3 of)arctan(x)

\int_{1}^{3} arctan (x) d x

integral of (x+1)/(x^2+16)

\int \frac{x + 1}{x ^{2} + 16} d x

derivative of f(x)=sqrt(x)(x-4)derivative of

f (x) = x (x - 4)

y^{''}+2y^'+y=10e^{-t}

y^{^{''}} + 2 y^{^{'}} + y = 10 e^{- t}

derivative of-2xe^{-2x}

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

Frequently Asked Questions (FAQ)

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