en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1+x^2

Solution

integral

1 + x^{2}

Solution

x + \frac{x ^{3}}{3} + C

Solution steps

\int 1 + 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

= \int 1 d x + \int x^{2} d x

\int 1 d x = x

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

= x + \frac{x ^{3}}{3}

Add a constant to the solution

= x + \frac{x ^{3}}{3} + C

Popular Examples

integral of e^xsqrt(37+e^x)

\int e^{x} 37 + e^{x} d x

integral of (ln(x))/((x-2)^2)

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

integral of ycos(x)+2xe^y

\int y cos (x) + 2 x e^{y} d x

integral of sin(2x)sqrt(2-3sin^2(x))

\int sin (2 x) 2 - 3 sin^{2} (x) d x

integral of (1+4x)/(sqrt(1+3x+6x^2))

\int \frac{1 + 4 x}{1 + 3 x + 6 x ^{2}} d x

Frequently Asked Questions (FAQ)

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