What is the integral of (6e^{5x}-7/x) ?

The integral of (6e^{5x}-7/x) is 6/5 e^{5x}-7ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (6e^{5x}-7/x)

\int (6 e^{5 x} - \frac{7}{x}) d x

\frac{6}{5} e^{5 x} - 7 ln ∣ x ∣ + C

Solution steps

\int 6 e^{5 x} - \frac{7}{x} d x

Apply the Sum Rule:

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

= \int 6 e^{5 x} d x - \int \frac{7}{x} d x

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

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= \frac{6}{5} e^{5 x} - 7 ln ∣ x ∣

Add a constant to the solution

= \frac{6}{5} e^{5 x} - 7 ln ∣ x ∣ + C

\frac{d}{d x} (\frac{6 x - 3}{x - 3})

\int sin (6 t) d t

\frac{d}{d x} (\frac{sin ( 0.5 x )}{x})

\int - \frac{2000 x}{( 1 + x ^{2} )} d x

x \to 0 + lim (sinh (x) cot (x))

What is the integral of (6e^{5x}-7/x) ?
The integral of (6e^{5x}-7/x) is 6/5 e^{5x}-7ln|x|+C