Mister Exam

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Integral of d{x}:
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Integral of x^4lnx
Integral of x*dx/(x^2-1)
Identical expressions
x/(9x^ four + one)
x divide by (9x to the power of 4 plus 1)
x divide by (9x to the power of four plus one)
x/(9x4+1)
x/9x4+1
x/(9x⁴+1)
x/9x^4+1
x divide by (9x^4+1)
x/(9x^4+1)dx
Similar expressions
x/(9x^4-1)

Solving integrals/ x/(9x^4+1)

Integral of x/(9x^4+1) dx

The solution

You have entered [src]

  1            
  /            
 |             
 |     x       
 |  -------- dx
 |     4       
 |  9*x  + 1   
 |             
/              
0

$$\int\limits_{0}^{1} \frac{x}{9 x^{4} + 1}\, dx$$

Integral(x/(9*x^4 + 1), (x, 0, 1))

Detail solution

Let $u = x^{2}$ .

Then let $du = 2 x dx$ and substitute $du$ :

$\int \frac{1}{18 u^{2} + 2}\, du$
1. The integral of $\frac{1}{u^{2} + 1}$ is $\frac{\operatorname{atan}{\left(3 u \right)}}{6}$ .
Now substitute $u$ back in:

$\frac{\operatorname{atan}{\left(3 x^{2} \right)}}{6}$
Add the constant of integration:

$\frac{\operatorname{atan}{\left(3 x^{2} \right)}}{6}+ \mathrm{constant}$

The answer is:

$\frac{\operatorname{atan}{\left(3 x^{2} \right)}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                       /   2\
 |    x              atan\3*x /
 | -------- dx = C + ----------
 |    4                  6     
 | 9*x  + 1                    
 |                             
/

$$\int \frac{x}{9 x^{4} + 1}\, dx = C + \frac{\operatorname{atan}{\left(3 x^{2} \right)}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

atan(3)
-------
   6

$$\frac{\operatorname{atan}{\left(3 \right)}}{6}$$

atan(3)
-------
   6

$$\frac{\operatorname{atan}{\left(3 \right)}}{6}$$

Упростить

Numerical answer [src]

0.208174295399709

0.208174295399709

The graph

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

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Identical expressions

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Integral of x/(9x^4+1) dx

Limits of integration:

The graph:

Piecewise:

The solution