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Popular >

integral of x-sin(x)

Solution

\int x - sin (x) d x

Solution

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

Popular Examples

integral of z/(e^{9z)}

\int \frac{z}{e ^{9 z}} d z

integral of x^5ln(x^7)

\int x^{5} ln (x^{7}) d x

integral of (e^{sqrt(2x)})/(sqrt(2x))

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

integral of xsqrt(ax+b)

\int x a x + b d x

integral of 1/(sqrt(2θ-θ^2))

\int \frac{1}{2 θ - θ ^{2}} d θ

Frequently Asked Questions (FAQ)

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