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

The integral of (3-x)/2 is 1/2 (3x-(x^2)/2)+C

Popular >

integral of (3-x)/2

\int \frac{3 - x}{2} d x

\frac{1}{2} (3 x - \frac{x ^{2}}{2}) + C

Solution steps

\int \frac{3 - x}{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 3 - x 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 3 d x - \int x d x)

\int 3 d x = 3 x

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

= \frac{1}{2} (3 x - \frac{x ^{2}}{2})

Add a constant to the solution

= \frac{1}{2} (3 x - \frac{x ^{2}}{2}) + C

\int \frac{2 x - 1}{( x - 2 ) ( x - 3 ) ( x + 1 )} d x

\int (a^{2} - 2 x^{2})^{4} \cdot (20 x) d x

\int \frac{2 x ^{3}}{1 + x ^{2}} d x

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

\int \frac{4 x}{1 - x ^{2}} d x