What is the integral of ze^{xz} ?

The integral of ze^{xz} is e^{zx}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ze^{xz}

\int z e^{x z} d x

e^{z x} + C

Solution steps

\int z e^{x z} d x

Take the constant out:

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

= z \cdot \int e^{z x} d x

Apply u-substitution

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

= z \cdot \int \frac{e ^{u}}{z} d u

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = z x

= z \frac{1}{z} e^{z x}

Simplify

z \frac{1}{z} e^{z x} : e^{z x}

= e^{z x}

Add a constant to the solution

= e^{z x} + C

\int x sin^{2} (ln (x)) d x

\int 3 x 2 x + 1 d x

\int \frac{8}{x} + 6 x d x

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

\int \frac{5}{x} - 6 e^{x} d x