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Popular >

integral of (x+2)/2

Solution

\int \frac{x + 2}{2} d x

Solution

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

Solution steps

\int \frac{x + 2}{2} 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 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int x d x + \int 2 d x)

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

\int 2 d x = 2 x

= \frac{1}{2} (\frac{x ^{2}}{2} + 2 x)

Simplify

\frac{1}{2} (\frac{x ^{2}}{2} + 2 x) : \frac{x ^{2}}{4} + x

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

Add a constant to the solution

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

Popular Examples

integral of (20(1-x^2))/(1+x^2)

\int \frac{20 ( 1 - x ^{2} )}{1 + x ^{2}} d x

integral of ((x))/x

\int \frac{( x )}{x} d x

integral of sin^6((3x)/2)

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

integral of (8/3)

\int (\frac{8}{3}) d m

integral of (sqrt(t^2+2t-3))/((t+1)^4)

\int \frac{t ^{2} + 2 t - 3}{( t + 1 ) ^{4}} d t

Frequently Asked Questions (FAQ)

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