What is the integral of e^xcos(2e^x) ?

The integral of e^xcos(2e^x) is 1/2 sin(2e^x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^xcos(2e^x)

\int e^{x} cos (2 e^{x}) d x

\frac{1}{2} sin (2 e^{x}) + C

Solution steps

\int e^{x} cos (2 e^{x}) d x

Apply u-substitution

= \int \frac{cos ( u )}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{2} sin (u)

Substitute back

u = 2 e^{x}

= \frac{1}{2} sin (2 e^{x})

Add a constant to the solution

= \frac{1}{2} sin (2 e^{x}) + C

\frac{d ^{2}}{d x ^{2}} (x^{9} e^{x})

\int 5 t sin^{2} (t) d t

\int 12 x^{2} + 6 x - 5 d x

\int_{0}^{\frac{π}{4}} tan^{8} (θ) sec^{2} (θ) d θ

\frac{e ^{x}}{ln ( x )}

What is the integral of e^xcos(2e^x) ?
The integral of e^xcos(2e^x) is 1/2 sin(2e^x)+C