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Identical expressions
one /((2x+ three)(sqrt(ln(2x+ three))))
1 divide by ((2x plus 3)( square root of (ln(2x plus 3))))
one divide by ((2x plus three)( square root of (ln(2x plus three))))
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1 divide by ((2x+3)(sqrt(ln(2x+3))))
1/((2x+3)(sqrt(ln(2x+3))))dx
Similar expressions
1/((2x-3)(sqrt(ln(2x+3))))
1/((2x+3)(sqrt(ln(2x-3))))

Solving integrals/ 1/((2x+3)(sqrt(ln(2x+3))))

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

The solution

You have entered [src]

  1                              
  /                              
 |                               
 |              1                
 |  -------------------------- dx
 |              ______________   
 |  (2*x + 3)*\/ log(2*x + 3)    
 |                               
/                                
0

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

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

Detail solution

There are multiple ways to do this integral.
Method #1
1. Rewrite the integrand:
  
  $\frac{1}{\left(2 x + 3\right) \sqrt{\log{\left(2 x + 3 \right)}}} = \frac{1}{2 x \sqrt{\log{\left(2 x + 3 \right)}} + 3 \sqrt{\log{\left(2 x + 3 \right)}}}$
2. Let $u = \sqrt{\log{\left(2 x + 3 \right)}}$ .
  
  Then let $du = \frac{dx}{\left(2 x + 3\right) \sqrt{\log{\left(2 x + 3 \right)}}}$ and substitute $du$ :
  
  $\int 1\, du$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, du = u$
  Now substitute $u$ back in:
  
  $\sqrt{\log{\left(2 x + 3 \right)}}$
Method #2
1. Rewrite the integrand:
  
  $\frac{1}{\left(2 x + 3\right) \sqrt{\log{\left(2 x + 3 \right)}}} = \frac{1}{2 x \sqrt{\log{\left(2 x + 3 \right)}} + 3 \sqrt{\log{\left(2 x + 3 \right)}}}$
2. Let $u = \sqrt{\log{\left(2 x + 3 \right)}}$ .
  
  Then let $du = \frac{dx}{\left(2 x + 3\right) \sqrt{\log{\left(2 x + 3 \right)}}}$ and substitute $du$ :
  
  $\int 1\, du$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, du = u$
  Now substitute $u$ back in:
  
  $\sqrt{\log{\left(2 x + 3 \right)}}$
Add the constant of integration:

$\sqrt{\log{\left(2 x + 3 \right)}}+ \mathrm{constant}$

The answer is:

$\sqrt{\log{\left(2 x + 3 \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

  ________     ________
\/ log(5)  - \/ log(3)

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

  ________     ________
\/ log(5)  - \/ log(3)

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

sqrt(log(5)) - sqrt(log(3))

Numerical answer [src]

0.220489167211315

0.220489167211315

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2