Integral of f(2x-1)(3x+4)dx dx

The solution

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$$\int\limits_{0}^{1} f \left(2 x - 1\right) \left(3 x + 4\right) 1\, dx$$

Integral(f*(2*x - 1*1)*(3*x + 4)*1, (x, 0, 1))

Detail solution

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

$\int f \left(2 x - 1\right) \left(3 x + 4\right) 1\, dx = f \int \left(2 x - 1\right) \left(3 x + 4\right)\, dx$
1. Rewrite the integrand:
  
  $\left(2 x - 1\right) \left(3 x + 4\right) = 6 x^{2} + 5 x - 4$
2. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 6 x^{2}\, dx = 6 \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $2 x^{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 5 x\, dx = 5 \int x\, dx$
    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: $\frac{5 x^{2}}{2}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(-4\right)\, dx = - 4 x$
  The result is: $2 x^{3} + \frac{5 x^{2}}{2} - 4 x$
So, the result is: $f \left(2 x^{3} + \frac{5 x^{2}}{2} - 4 x\right)$
Now simplify:

$\frac{f x \left(4 x^{2} + 5 x - 8\right)}{2}$
Add the constant of integration:

$\frac{f x \left(4 x^{2} + 5 x - 8\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{f x \left(4 x^{2} + 5 x - 8\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   /                 2\
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 | f*(2*x - 1)*(3*x + 4)*1 dx = C + f*|-4*x + 2*x  + ----|
 |                                    \               2  /
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$${{f\,\left(4\,x^3+5\,x^2-8\,x\right)}\over{2}}$$

Simplify

The answer [src]

f
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2

$${{f}\over{2}}$$

f
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2

$$\frac{f}{2}$$

Simplify

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

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Integral of f(2x-1)(3x+4)dx dx

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