What is the integral of cos(y)sqrt(e^y) ?

The integral of cos(y)sqrt(e^y) is 2/5 e^{y/2}cos(y)+4/5 e^{y/2}sin(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(y)sqrt(e^y)

\int cos (y) e^{y} d y

\frac{2}{5} e^{\frac{y}{2}} cos (y) + \frac{4}{5} e^{\frac{y}{2}} sin (y) + C

Solution steps

\int cos (y) e^{y} d y

Apply Integration By Parts

: e^{\frac{y}{2}} sin (y) - \int \frac{1}{2} e^{\frac{y}{2}} sin (y) d y

= e^{\frac{y}{2}} sin (y) - \int \frac{1}{2} e^{\frac{y}{2}} sin (y) d y

\int \frac{1}{2} e^{\frac{y}{2}} sin (y) d y = - \frac{2}{5} e^{\frac{y}{2}} cos (y) + \frac{1}{5} e^{\frac{y}{2}} sin (y)

= e^{\frac{y}{2}} sin (y) - (- \frac{2}{5} e^{\frac{y}{2}} cos (y) + \frac{1}{5} e^{\frac{y}{2}} sin (y))

Simplify

e^{\frac{y}{2}} sin (y) - (- \frac{2}{5} e^{\frac{y}{2}} cos (y) + \frac{1}{5} e^{\frac{y}{2}} sin (y)) : \frac{2}{5} e^{\frac{y}{2}} cos (y) + \frac{4}{5} e^{\frac{y}{2}} sin (y)

= \frac{2}{5} e^{\frac{y}{2}} cos (y) + \frac{4}{5} e^{\frac{y}{2}} sin (y)

Add a constant to the solution

= \frac{2}{5} e^{\frac{y}{2}} cos (y) + \frac{4}{5} e^{\frac{y}{2}} sin (y) + C

\int e^{5 x - 2} d x

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

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

\int \frac{cos ( x )}{( 1 + sin ( x ) ) ^{2}} d x

\int \frac{ln ( ln ( 4 x ) )}{x ln ( 4 x )} d x

What is the integral of cos(y)sqrt(e^y) ?
The integral of cos(y)sqrt(e^y) is 2/5 e^{y/2}cos(y)+4/5 e^{y/2}sin(y)+C