What is the integral of e^8xcos(x) ?

The integral of e^8xcos(x) is e^8(xsin(x)+cos(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^8xcos(x)

integral

e^{8} x cos (x)

e^{8} (x sin (x) + cos (x)) + C

Solution steps

\int e^{8} x cos (x) d x

Take the constant out:

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

= e^{8} \cdot \int x cos (x) d x

Apply Integration By Parts

= e^{8} (x sin (x) - \int sin (x) d x)

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

= e^{8} (x sin (x) - (- cos (x)))

Simplify

= e^{8} (x sin (x) + cos (x))

Add a constant to the solution

= e^{8} (x sin (x) + cos (x)) + C

What is the integral of e^8xcos(x) ?
The integral of e^8xcos(x) is e^8(xsin(x)+cos(x))+C