What is the integral of cos(z/y) ?

The integral of cos(z/y) is ysin(z/y)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(z/y)

\int cos (\frac{z}{y}) d z

y sin (\frac{z}{y}) + C

Solution steps

\int cos (\frac{z}{y}) d z

Apply u-substitution

: \int cos (u) y d u

= \int cos (u) y d u

Take the constant out:

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

= y \cdot \int cos (u) d u

Use the common integral:

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

= y sin (u)

Substitute back

u = \frac{z}{y}

= y sin (\frac{z}{y})

Add a constant to the solution

= y sin (\frac{z}{y}) + C

f (x) = - 3 x^{2} - 2 x^{2} - 1, at x = - 1

\int \frac{cos ( x )}{5 + sin ( x )} d x

11 t^{2} + 9

\int_{0}^{3} \frac{1}{x ^{2} - 6 x + 5} d x

\frac{6 x}{( x ^{2} + 3 ) ^{2}}