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Popular >

integral of sin(y)+y

Solution

\int sin (y) + y d y

Solution

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

Solution steps

\int sin (y) + y d y

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 (y) d y + \int y d y

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

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

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

Add a constant to the solution

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

Popular Examples

integral of (-3)/x-9/(x^2)

\int \frac{- 3}{x} - \frac{9}{x ^{2}} d x

integral of (2x-3)/(x^2+2x+5)

\int \frac{2 x - 3}{x ^{2} + 2 x + 5} d x

integral of-cos^3(t)

\int - cos^{3} (t) d t

integral of (11x+8)/(10x^2+5x)

\int \frac{11 x + 8}{10 x ^{2} + 5 x} d x

integral of 1/(sqrt(x^2+R^2))

\int \frac{1}{x ^{2} + R ^{2}} d x

Frequently Asked Questions (FAQ)

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