What is the integral of e^x+1/2+2x^2+3 ?

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

integral

e^{x} + \frac{1}{2} + 2 x^{2} + 3

\frac{2 x ^{3}}{3} + \frac{7}{2} x + e^{x} + C

Solution steps

\int e^{x} + \frac{1}{2} + 2 x^{2} + 3 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 e^{x} d x + \int \frac{1}{2} d x + \int 2 x^{2} d x + \int 3 d x

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

\int \frac{1}{2} d x = \frac{1}{2} x

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

\int 3 d x = 3 x

= e^{x} + \frac{1}{2} x + \frac{2 x ^{3}}{3} + 3 x

Simplify

e^{x} + \frac{1}{2} x + \frac{2 x ^{3}}{3} + 3 x : \frac{2 x ^{3}}{3} + \frac{7}{2} x + e^{x}

= \frac{2 x ^{3}}{3} + \frac{7}{2} x + e^{x}

Add a constant to the solution

= \frac{2 x ^{3}}{3} + \frac{7}{2} x + e^{x} + C

\frac{1}{x ^{2} + 9}

(3 x - 1)^{- 2}

x^{4} \cdot n^{- 1} \cdot 1 - x^{2}

y = 2 e^{4} x + 3

- 3 sec (x) \cdot sec^{3} (x)

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