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Popular Calculus >

integral of (-x+1)

Solution

\int (- x + 1) d x

Solution

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

Solution steps

\int - x + 1 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 1 d x

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

\int 1 d x = x

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

Add a constant to the solution

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

Graph

Popular Examples

integral of log_{10}(x^2+1)

\int lo g_{10} (x^{2} + 1) d x

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

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

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

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

integral of (ln(arctan(x)))/(1+x^2)

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

integral of 1/(4x^3+4x^2+x)

\int \frac{1}{4 x ^{3} + 4 x ^{2} + x} d x

Frequently Asked Questions (FAQ)

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