What is the integral of 4/(5-2i) ?

The integral of 4/(5-2i) is -4/29+i 20/29+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4/(5-2i)

\int \frac{4}{5 - 2 i} d i

- \frac{4}{29} + i \frac{20}{29} + C

Solution steps

\int \frac{4}{5 - 2 i} d i

Take the constant out:

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

= 4 \cdot \int \frac{1}{5 - 2 i} d i

Expand

\frac{1}{5 - 2 i} : \frac{5}{29} + \frac{2 i}{29}

= 4 \cdot \int \frac{5}{29} + \frac{2 i}{29} d i

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 4 (\int \frac{5}{29} d i + \int \frac{2 i}{29} d i)

\int \frac{5}{29} d i = \frac{5}{29} i

\int \frac{2 i}{29} d i = - \frac{1}{29}

= 4 (\frac{5}{29} i - \frac{1}{29})

Rewrite

4 (\frac{5}{29} i - \frac{1}{29})

in standard complex form:

- \frac{4}{29} + \frac{20}{29} i

Add a constant to the solution

= - \frac{4}{29} + i \frac{20}{29} + C

\int cot^{2} (θ) csc^{2} (θ) d θ

\int 1 + tan (h^{2}) x d x

\int \frac{x ^{2} + 1}{( x ^{2} - 4 ) ( x + 2 )} d x

\int 2 x e^{x - 1} d x

\int \frac{( u ^{2} + 1 ) ^{2}}{u ^{2}} d u