What is the integral from 1 to 6 of (2x^3+5x^2+2x+8) ?

The integral from 1 to 6 of (2x^3+5x^2+2x+8) is 6485/6

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integral from 1 to 6 of (2x^3+5x^2+2x+8)

\int_{1}^{6} (2 x^{3} + 5 x^{2} + 2 x + 8) d x

\frac{6485}{6}

Decimal Notation

1080.83333 \dots

Solution steps

\int_{1}^{6} 2 x^{3} + 5 x^{2} + 2 x + 8 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}^{6} 2 x^{3} d x + \int_{1}^{6} 5 x^{2} d x + \int_{1}^{6} 2 x d x + \int_{1}^{6} 8 d x

\int_{1}^{6} 2 x^{3} d x = \frac{1295}{2}

\int_{1}^{6} 5 x^{2} d x = \frac{1075}{3}

\int_{1}^{6} 2 x d x = 35

\int_{1}^{6} 8 d x = 40

= \frac{1295}{2} + \frac{1075}{3} + 35 + 40

Simplify

\frac{1295}{2} + \frac{1075}{3} + 35 + 40 : \frac{6485}{6}

= \frac{6485}{6}

x \to 3 + lim (\frac{1}{6 - 2 x})

f (x) = 1.1 x + e^{x}, at x = 0

\int \frac{x ^{2}}{x ^{4} - 6 x ^{2} - 27} d x

y y^{^{'}} + 36 x = 0

\frac{d}{d x} ((8 x^{2} - 16 x + 16) e^{x})

What is the integral from 1 to 6 of (2x^3+5x^2+2x+8) ?
The integral from 1 to 6 of (2x^3+5x^2+2x+8) is 6485/6