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Popular >

integral of 1/2-x

Solution

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

Solution

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

Solution steps

\int \frac{1}{2} - 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

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of 7/(4sqrt(x^6))

\int \frac{7}{4 x ^{6}} d x

integral of (e^2)/x-1/(sqrt(1-x^2))

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

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

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

integral of 1/6 x^6

\int \frac{1}{6} x^{6} d x

integral of (e^{3x}+6e^{-x})

\int (e^{3 x} + 6 e^{- x}) d x

Frequently Asked Questions (FAQ)

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