What is the integral from-1 to 7 of 3x+7-x^2+3x ?

The integral from-1 to 7 of 3x+7-x^2+3x is 256/3

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integral from-1 to 7 of 3x+7-x^2+3x

\int_{- 1}^{7} 3 x + 7 - x^{2} + 3 x d x

\frac{256}{3}

Decimal Notation

85.33333 \dots

Solution steps

\int_{- 1}^{7} 3 x + 7 - x^{2} + 3 x d x

Simplify

= \int_{- 1}^{7} - x^{2} + 6 x + 7 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}^{7} x^{2} d x + \int_{- 1}^{7} 6 x d x + \int_{- 1}^{7} 7 d x

\int_{- 1}^{7} x^{2} d x = \frac{344}{3}

\int_{- 1}^{7} 6 x d x = 144

\int_{- 1}^{7} 7 d x = 56

= - \frac{344}{3} + 144 + 56

Simplify

- \frac{344}{3} + 144 + 56 : \frac{256}{3}

= \frac{256}{3}

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

\frac{d N}{d t} + N = Nt e^{t + 2}

\int \frac{x ^{4}}{x ^{3} - 1} d x

y = \frac{4}{4 - x ^{2}}, (0, 1)

What is the integral from-1 to 7 of 3x+7-x^2+3x ?
The integral from-1 to 7 of 3x+7-x^2+3x is 256/3