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Popular Calculus >

integral of-x+3

Solution

\int - x + 3 d x

Solution

- \frac{x ^{2}}{2} + 3 x + C

Solution steps

\int - x + 3 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 3 d x

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

\int 3 d x = 3 x

= - \frac{x ^{2}}{2} + 3 x

Add a constant to the solution

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

Graph

Popular Examples

integral of (x^6+sec^2(x))

\int (x^{6} + sec^{2} (x)) d x

integral of 1/(xsqrt((x+1)))

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

derivative of 3x^{2x}

d er i v a t i v e 3 x^{2 x}

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

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

derivative of y=(sqrt(x))/(x+1)

d er i v a t i v e y = \frac{x}{x + 1}

Frequently Asked Questions (FAQ)

What is the integral of-x+3 ?
The integral of-x+3 is -(x^2)/2+3x+C