What is the integral of (x^5-5^x+\sqrt[5]{x}-5/x) ?

The integral of (x^5-5^x+\sqrt[5]{x}-5/x) is (x^6)/6-(5^x)/(ln(5))+5/6 x^{6/5}-5ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x^5-5^x+\sqrt[5]{x}-5/x)

\frac{x ^{6}}{6} - \frac{5 ^{x}}{ln ( 5 )} + \frac{5}{6} x^{\frac{6}{5}} - 5 ln ∣ x ∣ + C

Solution steps

Apply the Sum Rule:

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

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

\int 5^{x} d x = \frac{5 ^{x}}{ln ( 5 )}

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= \frac{x ^{6}}{6} - \frac{5 ^{x}}{ln ( 5 )} + \frac{5}{6} x^{\frac{6}{5}} - 5 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{6}}{6} - \frac{5 ^{x}}{ln ( 5 )} + \frac{5}{6} x^{\frac{6}{5}} - 5 ln ∣ x ∣ + C

What is the integral of (x^5-5^x+\sqrt[5]{x}-5/x) ?
The integral of (x^5-5^x+\sqrt[5]{x}-5/x) is (x^6)/6-(5^x)/(ln(5))+5/6 x^{6/5}-5ln|x|+C