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Popular >

integral of x-1/3

Solution

\int x - \frac{1}{3} d x

Solution

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

Solution steps

\int x - \frac{1}{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 \frac{1}{3} d x

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

\int \frac{1}{3} d x = \frac{1}{3} x

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

Add a constant to the solution

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

Popular Examples

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

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

integral of e^{4x}cos(-1x)

\int e^{4 x} cos (- 1 x) d x

integral of-x*sin(x)

\int - x \cdot sin (x) d x

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

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

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

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

Frequently Asked Questions (FAQ)

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