What is the integral of ((5x^3)/(2x^2)) ?

The integral of ((5x^3)/(2x^2)) is (5x^2)/4+C

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integral of ((5x^3)/(2x^2))

\int (\frac{5 x ^{3}}{2 x ^{2}}) d x

\frac{5 x ^{2}}{4} + C

Solution steps

\int \frac{5 x ^{3}}{2 x ^{2}} d x

Take the constant out:

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

= \frac{5}{2} \cdot \int \frac{x ^{3}}{x ^{2}} d x

Simplify

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

= \frac{5}{2} \cdot \int x d x

Apply the Power Rule

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

= \frac{5}{2} \cdot \frac{x ^{2}}{2}

Simplify

\frac{5}{2} \cdot \frac{x ^{2}}{2} : \frac{5 x ^{2}}{4}

= \frac{5 x ^{2}}{4}

Add a constant to the solution

= \frac{5 x ^{2}}{4} + C

n = 0 \sum \infty \frac{1}{n + 8}

3 x^{3} - 5 x^{2} + 5 x - 14

d y = \frac{b - y}{a} d x

\int (n x)^{\frac{1 - n}{n}} d x

\int \frac{x}{8 + 2 x - x ^{2}} d x

What is the integral of ((5x^3)/(2x^2)) ?
The integral of ((5x^3)/(2x^2)) is (5x^2)/4+C