Integral of ax+0.7 dx

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 |  (a*x + 7/10) dx
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$$\int\limits_{2}^{1} \left(a x + \frac{7}{10}\right)\, dx$$

Integral(a*x + 7/10, (x, 2, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int a x\, dx = a \int x\, dx$
  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: $\frac{a x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \frac{7}{10}\, dx = \frac{7 x}{10}$
The result is: $\frac{a x^{2}}{2} + \frac{7 x}{10}$
Now simplify:

$\frac{x \left(5 a x + 7\right)}{10}$
Add the constant of integration:

$\frac{x \left(5 a x + 7\right)}{10}+ \mathrm{constant}$

The answer is:

$\frac{x \left(5 a x + 7\right)}{10}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               2
 |                       7*x   a*x 
 | (a*x + 7/10) dx = C + --- + ----
 |                        10    2  
/

$$\int \left(a x + \frac{7}{10}\right)\, dx = C + \frac{a x^{2}}{2} + \frac{7 x}{10}$$

Simplify

The answer [src]

  7    3*a
- -- - ---
  10    2

$$- \frac{3 a}{2} - \frac{7}{10}$$

  7    3*a
- -- - ---
  10    2

$$- \frac{3 a}{2} - \frac{7}{10}$$

-7/10 - 3*a/2

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