What is the integral of (e^x-5x^2)/7 ?

The integral of (e^x-5x^2)/7 is 1/7 (e^x-(5x^3)/3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (e^x-5x^2)/7

\int \frac{e ^{x} - 5 x ^{2}}{7} d x

\frac{1}{7} (e^{x} - \frac{5 x ^{3}}{3}) + C

Solution steps

\int \frac{e ^{x} - 5 x ^{2}}{7} d x

Take the constant out:

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

= \frac{1}{7} \cdot \int e^{x} - 5 x^{2} 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

= \frac{1}{7} (\int e^{x} d x - \int 5 x^{2} d x)

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

= \frac{1}{7} (e^{x} - \frac{5 x ^{3}}{3})

Add a constant to the solution

= \frac{1}{7} (e^{x} - \frac{5 x ^{3}}{3}) + C

\int \frac{x}{x ^{2} + x} d x

\int \frac{x ^{3}}{3 8 + x ^{4}} d x

\frac{9}{x}

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

\int \frac{2 x}{x ^{4}} d x

What is the integral of (e^x-5x^2)/7 ?
The integral of (e^x-5x^2)/7 is 1/7 (e^x-(5x^3)/3)+C