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

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

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integral of (4x^3)/(x^2)

\int \frac{4 x ^{3}}{x ^{2}} d x

2 x^{2} + C

Solution steps

\int \frac{4 x ^{3}}{x ^{2}} d x

Take the constant out:

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

= 4 \cdot \int \frac{x ^{3}}{x ^{2}} d x

Simplify

\frac{x ^{3}}{x ^{2}} : x

= 4 \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

= 2 x^{2}

Add a constant to the solution

= 2 x^{2} + C

\int 7 e^{x} 2 + e^{x} d x

\frac{d}{d x} (- \frac{1}{4} sin (\frac{x}{2}))

y = 2 x y^{^{'}}

(x + 1) (x^{3} + x - 2)

y^{^{'}} - \frac{6 y}{x} = (\frac{y}{x ^{2}})^{4}