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Identical expressions
((one /(x+ four))+sqrt(2x- three))
((1 divide by (x plus 4)) plus square root of (2x minus 3))
((one divide by (x plus four)) plus square root of (2x minus three))
((1/(x+4))+√(2x-3))
1/x+4+sqrt2x-3
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((1/(x+4))+sqrt(2x-3))dx
Similar expressions
((1/(x-4))+sqrt(2x-3))
((1/(x+4))+sqrt(2x+3))
((1/(x+4))-sqrt(2x-3))

Solving integrals/ ((1/(x+4))+sqrt(2x-3))

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

The solution

You have entered [src]

  1                         
  /                         
 |                          
 |  /  1       _________\   
 |  |----- + \/ 2*x - 3 | dx
 |  \x + 4              /   
 |                          
/                           
0

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

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

Detail solution

Integrate term-by-term:
1. Let $u = 2 x - 3$ .
  
  Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :
  
  $\int \frac{\sqrt{u}}{2}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \sqrt{u}\, du = \frac{\int \sqrt{u}\, du}{2}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
    So, the result is: $\frac{u^{\frac{3}{2}}}{3}$
  Now substitute $u$ back in:
  
  $\frac{\left(2 x - 3\right)^{\frac{3}{2}}}{3}$
1. Let $u = x + 4$ .
  
  Then let $du = dx$ and substitute $du$ :
  
  $\int \frac{1}{u}\, du$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  Now substitute $u$ back in:
  
  $\log{\left(x + 4 \right)}$
The result is: $\frac{\left(2 x - 3\right)^{\frac{3}{2}}}{3} + \log{\left(x + 4 \right)}$
Now simplify:

$\frac{\left(2 x - 3\right)^{\frac{3}{2}}}{3} + \log{\left(x + 4 \right)}$
Add the constant of integration:

$\frac{\left(2 x - 3\right)^{\frac{3}{2}}}{3} + \log{\left(x + 4 \right)}+ \mathrm{constant}$

The answer is:

$\frac{\left(2 x - 3\right)^{\frac{3}{2}}}{3} + \log{\left(x + 4 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                        
 |                                         3/2             
 | /  1       _________\          (2*x - 3)                
 | |----- + \/ 2*x - 3 | dx = C + ------------ + log(x + 4)
 | \x + 4              /               3                   
 |                                                         
/

$$\int \left(\sqrt{2 x - 3} + \frac{1}{x + 4}\right)\, dx = C + \frac{\left(2 x - 3\right)^{\frac{3}{2}}}{3} + \log{\left(x + 4 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

          I       ___         
-log(4) - - + I*\/ 3  + log(5)
          3

$$- \log{\left(4 \right)} + \log{\left(5 \right)} - \frac{i}{3} + \sqrt{3} i$$

          I       ___         
-log(4) - - + I*\/ 3  + log(5)
          3

$$- \log{\left(4 \right)} + \log{\left(5 \right)} - \frac{i}{3} + \sqrt{3} i$$

-log(4) - i/3 + i*sqrt(3) + log(5)

Numerical answer [src]

(0.22314355131421 + 1.39871747423554j)

(0.22314355131421 + 1.39871747423554j)

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution