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

The integral from 1 to 3 of (x^2+2x+1) is 56/3

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

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

\frac{56}{3}

Decimal

18.66666 \dots

Solution steps

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

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} 2 x d x = 8

\int_{1}^{3} 1 d x = 2

= \frac{26}{3} + 8 + 2

Simplify

\frac{26}{3} + 8 + 2 : \frac{56}{3}

= \frac{56}{3}

\int_{0}^{2} 2 e^{- 2 x} d x

\int_{0}^{\infty} x \cdot e^{- 3 x} d x

\int_{- 2}^{2} 4 x^{2} d x

\int_{- 3}^{3} (x^{2} - 2)^{2} d x

\int_{- 1}^{4} ∣ x - 1 ∣ d x

What is the integral from 1 to 3 of (x^2+2x+1) ?
The integral from 1 to 3 of (x^2+2x+1) is 56/3