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Popular >

integral of sin(x)-x

Solution

\int sin (x) - x d x

Solution

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

Solution steps

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

\int sin (x) d x = - cos (x)

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

= - cos (x) - \frac{x ^{2}}{2}

Add a constant to the solution

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

Popular Examples

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

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

integral of x/(sqrt(x^2+8^2))

\int \frac{x}{x ^{2} + 8 ^{2}} d x

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

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

integral of 1/5 e^x

\int \frac{1}{5} e^{x} d x

integral of (ax+by)

\int (a x + b y) d x

Frequently Asked Questions (FAQ)

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