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Popular >

integral of x+sin(y)

Solution

\int x + sin (y) d x

Solution

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

Solution steps

\int x + sin (y) 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 (y) d x + \int x d x

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

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

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

Add a constant to the solution

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

Popular Examples

integral of ((3-x))/(16+6x-x^2)

\int \frac{( 3 - x )}{16 + 6 x - x ^{2}} d x

integral of (9x+15)/(x^2+2x+1)

\int \frac{9 x + 15}{x ^{2} + 2 x + 1} d x

integral of 12(x^2+1)(x^3+3x)^3

\int 12 (x^{2} + 1) (x^{3} + 3 x)^{3} d x

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

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

integral of (2y)/((1-y)^7)

\int \frac{2 y}{( 1 - y ) ^{7}} d y

Frequently Asked Questions (FAQ)

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