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Popular Calculus >

integral of x+cos(x)

Solution

\int x + cos (x) d x

Solution

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

Solution steps

\int x + cos (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 cos (x) d x

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

derivative of 2xsec(x)

derivative of (x+2^x)

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

integral of (e^x)/((5-e^x)^2)

Frequently Asked Questions (FAQ)

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