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Popular >

integral of x+1/2

Solution

\int x + \frac{1}{2} d x

Solution

\frac{x ^{2}}{2} + \frac{1}{2} x + C

Solution steps

\int x + \frac{1}{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

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

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

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

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

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{1}{2} x + C

Popular Examples

integral of x(1)

\int x (1) d x

integral of (sin(x))/(3-cos(x))

\int \frac{sin ( x )}{3 - cos ( x )} d x

integral of 1/(4+7x^2)

\int \frac{1}{4 + 7 x ^{2}} d x

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

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

integral of 4+x

\int 4 + x d x

Frequently Asked Questions (FAQ)

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