What is the integral from 0 to 3 of (1+2sqrt(x))^2 ?

The integral from 0 to 3 of (1+2sqrt(x))^2 is 21+8sqrt(3)

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integral from 0 to 3 of (1+2sqrt(x))^2

\int_{0}^{3} (1 + 2 x)^{2} d x

21 + 83

Decimal Notation

34.85640 \dots

Solution steps

\int_{0}^{3} (1 + 2 x)^{2} d x

Expand

(1 + 2 x)^{2} : 1 + 4 x + 4 x

= \int_{0}^{3} 1 + 4 x + 4 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_{0}^{3} 1 d x + \int_{0}^{3} 4 x d x + \int_{0}^{3} 4 x d x

\int_{0}^{3} 1 d x = 3

\int_{0}^{3} 4 x d x = 83

\int_{0}^{3} 4 x d x = 18

= 3 + 83 + 18

Simplify

= 21 + 83

\int_{0}^{1} x^{2} + x^{4} d x

\int_{1}^{5} - x^{2} + 4 x d x

\int_{0}^{1} \frac{x}{x ( 1 - x )} d x

\int_{1}^{3} (x^{2} + x + 4) d x

\int_{1}^{9} 3 x^{2} + x x + 1 d x

What is the integral from 0 to 3 of (1+2sqrt(x))^2 ?
The integral from 0 to 3 of (1+2sqrt(x))^2 is 21+8sqrt(3)