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1/((2x+5)^(3/4))dx
Similar expressions
1/((2x-5)^(3/4))

Integral of 1/((2x+5)^(3/4)) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |           3/4   
 |  (2*x + 5)      
 |                 
/                  
0

$$\int\limits_{0}^{1} \frac{1}{\left(2 x + 5\right)^{\frac{3}{4}}}\, dx$$

Integral(1/((2*x + 5)^(3/4)), (x, 0, 1))

Detail solution

Let $u = \left(2 x + 5\right)^{\frac{3}{4}}$ .

Then let $du = \frac{3 dx}{2 \sqrt[4]{2 x + 5}}$ and substitute $\frac{2 du}{3}$ :

$\int \frac{2}{3 u^{\frac{2}{3}}}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u^{\frac{2}{3}}}\, du = \frac{2 \int \frac{1}{u^{\frac{2}{3}}}\, du}{3}$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{u^{\frac{2}{3}}}\, du = 3 \sqrt[3]{u}$
  So, the result is: $2 \sqrt[3]{u}$
Now substitute $u$ back in:

$2 \sqrt[4]{2 x + 5}$
Now simplify:

$2 \sqrt[4]{2 x + 5}$
Add the constant of integration:

$2 \sqrt[4]{2 x + 5}+ \mathrm{constant}$

The answer is:

$2 \sqrt[4]{2 x + 5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                                    
 |      1                  4 _________
 | ------------ dx = C + 2*\/ 2*x + 5 
 |          3/4                       
 | (2*x + 5)                          
 |                                    
/

$$\int \frac{1}{\left(2 x + 5\right)^{\frac{3}{4}}}\, dx = C + 2 \sqrt[4]{2 x + 5}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    4 ___     4 ___
- 2*\/ 5  + 2*\/ 7

$$- 2 \sqrt[4]{5} + 2 \sqrt[4]{7}$$

    4 ___     4 ___
- 2*\/ 5  + 2*\/ 7

$$- 2 \sqrt[4]{5} + 2 \sqrt[4]{7}$$

-2*5^(1/4) + 2*7^(1/4)

Numerical answer [src]

0.26245556095313

0.26245556095313

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

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Identical expressions

Similar expressions

Integral of 1/((2x+5)^(3/4)) dx

Limits of integration:

The graph:

Piecewise:

The solution