What is the integral of ycos((y^2)/(x^2)) ?

The integral of ycos((y^2)/(x^2)) is (x^2)/2 sin((y^2)/(x^2))+C

integral of ycos((y^2)/(x^2))

\int y cos (\frac{y ^{2}}{x ^{2}}) d y

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

Solution steps

\int y cos (\frac{y ^{2}}{x ^{2}}) d y

Apply u-substitution

= \int \frac{x ^{2} cos ( u )}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{x ^{2}}{2} \cdot \int cos (u) d u

Use the common integral:

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

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

Substitute back

u = \frac{y ^{2}}{x ^{2}}

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

Add a constant to the solution

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

a re a x^{2} - 43, 5 - 2 x

\int \frac{x ^{2} - 8 x - 13}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

a re a 2 x = y^{2}, x + y = 4, x + y = 12

\frac{d}{d x} (x e^{x a})

x \to \infty lim (- 1^{x} x)

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