en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2(1+x)

Solution

\int 2 (1 + x) d x

Solution

2 x + x^{2} + C

Solution steps

\int 2 (1 + x) d x

Take the constant out:

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

= 2 \cdot \int 1 + 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

= 2 (\int 1 d x + \int x d x)

\int 1 d x = x

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

= 2 (x + \frac{x ^{2}}{2})

Simplify

2 (x + \frac{x ^{2}}{2}) : 2 x + x^{2}

= 2 x + x^{2}

Add a constant to the solution

= 2 x + x^{2} + C

Popular Examples

integral of sec(x)(sec(x)+tan(x))integral

sec (x) (sec (x) + tan (x))

integral of 1/(4x-4x^2)

\int \frac{1}{4 x - 4 x ^{2}} d x

integral of (sqrt(x-7))/(x+6)

\int \frac{x - 7}{x + 6} d x

integral of (x^6)/(sqrt(x^7-9))

\int \frac{x ^{6}}{x ^{7} - 9} d x

integral of (x+7)/(x(x+2)^2)

\int \frac{x + 7}{x ( x + 2 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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