Integral of 3(x-5) dt

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 |  3*(x - 5) dx
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$$\int\limits_{0}^{1} 3 \left(x - 5\right)\, dx$$

Integral(3*(x - 5), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 3 \left(x - 5\right)\, dx = 3 \int \left(x - 5\right)\, dx$
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(-5\right)\, dx = - 5 x$
  The result is: $\frac{x^{2}}{2} - 5 x$
So, the result is: $\frac{3 x^{2}}{2} - 15 x$
Now simplify:

$\frac{3 x \left(x - 10\right)}{2}$
Add the constant of integration:

$\frac{3 x \left(x - 10\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{3 x \left(x - 10\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             2
 |                           3*x 
 | 3*(x - 5) dx = C - 15*x + ----
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$$\int 3 \left(x - 5\right)\, dx = C + \frac{3 x^{2}}{2} - 15 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-27/2

$$- \frac{27}{2}$$

-27/2

$$- \frac{27}{2}$$

-27/2

Numerical answer [src]

-13.5

-13.5

Use the examples entering the upper and lower limits of integration.