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Identical expressions
(f^ one (x)+f^ two (x))
(f to the power of 1(x) plus f squared (x))
(f to the power of one (x) plus f to the power of two (x))
(f1(x)+f2(x))
f1x+f2x
(f^1(x)+f²(x))
(f to the power of 1(x)+f to the power of 2(x))
f^1x+f^2x
(f^1(x)+f^2(x))dx
Similar expressions
(f^1(x)-f^2(x))

Integral of (f^1(x)+f^2(x)) dx

The solution

You have entered [src]

  b                 
  /                 
 |                  
 |  / 1      2  \   
 |  \f *x + f *x/ dx
 |                  
/                   
a

$$\int\limits_{a}^{b} \left(f^{2} x + f^{1} x\right)\, dx$$

Integral(f^1*x + f^2*x, (x, a, b))

Detail solution

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

$\frac{f x^{2} \left(f + 1\right)}{2}$
Add the constant of integration:

$\frac{f x^{2} \left(f + 1\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{f x^{2} \left(f + 1\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                           2    2  2
 | / 1      2  \          f*x    f *x 
 | \f *x + f *x/ dx = C + ---- + -----
 |                         2       2  
/

$$\int \left(f^{2} x + f^{1} x\right)\, dx = C + \frac{f^{2} x^{2}}{2} + \frac{f x^{2}}{2}$$

Simplify

The answer [src]

   /     2\      /     2\
 2 |f   f |    2 |f   f |
b *|- + --| - a *|- + --|
   \2   2 /      \2   2 /

$$- a^{2} \left(\frac{f^{2}}{2} + \frac{f}{2}\right) + b^{2} \left(\frac{f^{2}}{2} + \frac{f}{2}\right)$$

   /     2\      /     2\
 2 |f   f |    2 |f   f |
b *|- + --| - a *|- + --|
   \2   2 /      \2   2 /

$$- a^{2} \left(\frac{f^{2}}{2} + \frac{f}{2}\right) + b^{2} \left(\frac{f^{2}}{2} + \frac{f}{2}\right)$$

b^2*(f/2 + f^2/2) - a^2*(f/2 + f^2/2)

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

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Integral of (f^1(x)+f^2(x)) dx

Limits of integration:

The graph:

Piecewise:

The solution