What is the integral of e^tcos(t) ?

The integral of e^tcos(t) is (e^tsin(t))/2+(e^tcos(t))/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^tcos(t)

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

\frac{e ^{t} sin ( t )}{2} + \frac{e ^{t} cos ( t )}{2} + C

Solution steps

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

Apply Integration By Parts

: e^{t} sin (t) - \int e^{t} sin (t) d t

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

Apply Integration By Parts

: - e^{t} cos (t) - \int - e^{t} cos (t) d t

= e^{t} sin (t) - (- e^{t} cos (t) - \int - e^{t} cos (t) d t)

Take the constant out:

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

= e^{t} sin (t) - (- e^{t} cos (t) - (- \int e^{t} cos (t) d t))

Therefore

\int e^{t} cos (t) d t = e^{t} sin (t) - (- e^{t} cos (t) - (- \int e^{t} cos (t) d t))

Isolate

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

= \frac{e ^{t} sin ( t )}{2} + \frac{e ^{t} cos ( t )}{2}

Add a constant to the solution

= \frac{e ^{t} sin ( t )}{2} + \frac{e ^{t} cos ( t )}{2} + C

\frac{d}{d x} (ln (x x^{2} - 6))

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

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

\frac{1}{2} x^{2} 49 - x^{2}

\int cos^{5} (x) sin (2 x) d x

What is the integral of e^tcos(t) ?
The integral of e^tcos(t) is (e^tsin(t))/2+(e^tcos(t))/2+C