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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

Graph

Popular Examples

integral of (36)/x

\int \frac{36}{x} d x

integral of 18x^5

\int 18 x^{5} d x

(d^4)/(dx^4)(17e^{x^2})

\frac{d ^{4}}{d x ^{4}} (17 e^{x^{2}})

integral of sqrt(3x-9)

\int 3 x - 9 d x

derivative of 1/(tan^2(x))

\frac{d}{d x} (\frac{1}{tan ^{2} ( 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