What is the integral of (5e^x+(10)/x-4x^3+2^x) ?

The integral of (5e^x+(10)/x-4x^3+2^x) is 5e^x+10ln|x|-x^4+(2^x)/(ln(2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5e^x+(10)/x-4x^3+2^x)

\int (5 e^{x} + \frac{10}{x} - 4 x^{3} + 2^{x}) d x

5 e^{x} + 10 ln ∣ x ∣ - x^{4} + \frac{2 ^{x}}{ln ( 2 )} + C

Solution steps

\int 5 e^{x} + \frac{10}{x} - 4 x^{3} + 2^{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 5 e^{x} d x + \int \frac{10}{x} d x - \int 4 x^{3} d x + \int 2^{x} d x

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

\int \frac{10}{x} d x = 10 ln ∣ x ∣

\int 4 x^{3} d x = x^{4}

\int 2^{x} d x = \frac{2 ^{x}}{ln ( 2 )}

= 5 e^{x} + 10 ln ∣ x ∣ - x^{4} + \frac{2 ^{x}}{ln ( 2 )}

Add a constant to the solution

= 5 e^{x} + 10 ln ∣ x ∣ - x^{4} + \frac{2 ^{x}}{ln ( 2 )} + C

\int sin^{2} (x) \cdot cos^{7} (x) d x

\int cos^{6} (π) x d x

\int e^{- \frac{1}{2} t^{2}} d t

\int sin (2 θ) sin (4 θ) d θ

\int (x^{2.7} + x^{- 1.3}) d x

What is the integral of (5e^x+(10)/x-4x^3+2^x) ?
The integral of (5e^x+(10)/x-4x^3+2^x) is 5e^x+10ln|x|-x^4+(2^x)/(ln(2))+C