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Integral of k*x+b dx

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$$\int\limits_{0}^{1} \left(b + k x\right)\, dx$$

Integral(k*x + b, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int b\, dx = b x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int k x\, dx = k \int x\, dx$
  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: $\frac{k x^{2}}{2}$
The result is: $b x + \frac{k x^{2}}{2}$
Now simplify:

$\frac{x \left(2 b + k x\right)}{2}$
Add the constant of integration:

$\frac{x \left(2 b + k x\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 b + k x\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

Simplify

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