What is the integral of (31+4/(x^3)-19e^x) ?

The integral of (31+4/(x^3)-19e^x) is 31x-2/(x^2)-19e^x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (31+4/(x^3)-19e^x)

\int (31 + \frac{4}{x ^{3}} - 19 e^{x}) d x

31 x - \frac{2}{x ^{2}} - 19 e^{x} + C

Solution steps

\int 31 + \frac{4}{x ^{3}} - 19 e^{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 31 d x + \int \frac{4}{x ^{3}} d x - \int 19 e^{x} d x

\int 31 d x = 31 x

\int \frac{4}{x ^{3}} d x = - \frac{2}{x ^{2}}

\int 19 e^{x} d x = 19 e^{x}

= 31 x - \frac{2}{x ^{2}} - 19 e^{x}

Add a constant to the solution

= 31 x - \frac{2}{x ^{2}} - 19 e^{x} + C

\int (5 x^{2} + \frac{1}{( 5 x ) ^{2}}) d x

\int 5 x e^{6 x^{2}} d x

\int - \frac{2}{y ^{3}} d y

\int 3 x^{2} (x^{3} + 1)^{3} d x

\int e^{2 s} d s

What is the integral of (31+4/(x^3)-19e^x) ?
The integral of (31+4/(x^3)-19e^x) is 31x-2/(x^2)-19e^x+C