en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-xsin(y)+sin(y)+ycos(y)

Solution

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

Solution

y sin (y) + x cos (y) + C

Solution steps

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

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

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

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

= - cos (y) + y sin (y) + cos (y) - (- x cos (y))

Simplify

= y sin (y) + x cos (y)

Add a constant to the solution

= y sin (y) + x cos (y) + C

Popular Examples

integral of x^2(10^{x^3})

\int x^{2} (1 0^{x^{3}}) d x

integral of (3x^2+1)/((x+1)(x-5)^2)

\int \frac{3 x ^{2} + 1}{( x + 1 ) ( x - 5 ) ^{2}} d x

integral of x(x-8)^{3/4}

\int x (x - 8)^{\frac{3}{4}} d x

integral of (3-x^2)

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

integral of (3^{2x+1})

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

Frequently Asked Questions (FAQ)

What is the integral of-xsin(y)+sin(y)+ycos(y) ?
The integral of-xsin(y)+sin(y)+ycos(y) is ysin(y)+xcos(y)+C