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Popular >

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

Popular Examples

derivative of 2xsec(x)

\frac{d}{d x} (2 x sec (x))

derivative of (x+2^x)

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

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

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

derivative of y=xsqrt(36-x^2)derivative of

y = x 36 - x^{2}

x y^{^{'}} + 3 y = x^{4} - x

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