What is the integral of cos(y)e^{5sin(y)} ?

The integral of cos(y)e^{5sin(y)} is 1/5 e^{5sin(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)e^{5sin(y)}

\int cos (y) e^{5 s i n (y)} d y

\frac{1}{5} e^{5 s i n (y)} + C

Solution steps

\int cos (y) e^{5 s i n (y)} d y

Apply u-substitution

: \int \frac{e ^{u}}{5} d u

= \int \frac{e ^{u}}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{5} e^{u}

Substitute back

u = 5 sin (y)

= \frac{1}{5} e^{5 s i n (y)}

Add a constant to the solution

= \frac{1}{5} e^{5 s i n (y)} + C

n = 0 \sum \infty \frac{1 ^{n}}{n !}

\int (5 + x^{3}) (4 - x^{2}) d x

\int (x^{\frac{3}{2}} + 7)^{6} x d x

x \to 5 lim (2)

x^{2} - x^{4}

What is the integral of cos(y)e^{5sin(y)} ?
The integral of cos(y)e^{5sin(y)} is 1/5 e^{5sin(y)}+C