What is the integral of (x^2)/2 (1/x) ?

The integral of (x^2)/2 (1/x) is (x^2)/4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int \frac{x ^{2}}{2} (\frac{1}{x}) d x

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

Solution steps

\int \frac{x ^{2}}{2} \cdot \frac{1}{x} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int x^{2} \frac{1}{x} d x

Simplify

x^{2} \frac{1}{x} : x

= \frac{1}{2} \cdot \int x d x

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{x ^{2}}{2}

Simplify

\frac{1}{2} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{4}

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

Add a constant to the solution

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

\int \frac{s + 1}{s ^{3} + s ^{2} - 6 s} d s

\int e^{(x)} d x

\int \frac{( 9 - x ^{2} ) ^{3}}{x ^{6}} d x

\int 30 + 0.2 x d x

\int sin^{8} (\frac{x}{6}) cos (\frac{x}{6}) d x

What is the integral of (x^2)/2 (1/x) ?
The integral of (x^2)/2 (1/x) is (x^2)/4+C