积分 x^2-8x+15/ dx

解答

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$$\int\limits_{0}^{1} \left(\left(x^{2} - 8 x\right) + 15\right)\, dx$$

Integral(x^2 - 8*x + 15, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 8 x\right)\, dx = - 8 \int x\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    So, the result is: $- 4 x^{2}$
  The result is: $\frac{x^{3}}{3} - 4 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 15\, dx = 15 x$
The result is: $\frac{x^{3}}{3} - 4 x^{2} + 15 x$
Now simplify:

$\frac{x \left(x^{2} - 12 x + 45\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 12 x + 45\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 12 x + 45\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | \x  - 8*x + 15/ dx = C - 4*x  + 15*x + --
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$$\int \left(\left(x^{2} - 8 x\right) + 15\right)\, dx = C + \frac{x^{3}}{3} - 4 x^{2} + 15 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

34/3

$$\frac{34}{3}$$

34/3

$$\frac{34}{3}$$

34/3

Numerical answer [src]

11.3333333333333

11.3333333333333

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积分 x^2-8x+15/ dx

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