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Popular >

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

Solution

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

Solution

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

Solution steps

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

Popular Examples

integral of (6y-7)/((2y+1)(4y^2+1))

\int \frac{6 y - 7}{( 2 y + 1 ) ( 4 y ^{2} + 1 )} d y

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\int \frac{7 x ^{2}}{( 144 + x ^{2} ) ^{2}} d x

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\int \frac{y + 4}{y - 4} d y

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\int x^{l n (3)} d x

integral of (5x^2)/((x-7)^3)

\int \frac{5 x ^{2}}{( x - 7 ) ^{3}} d x

Frequently Asked Questions (FAQ)

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