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dx/sqrt(1-16x^2)dx
Solving integrals/ dx/sqrt(1-16x^2)dx

You entered:

dx/sqrt(1-16x^2)dx

What you mean?

dx/((sqrt(1 - 16*x^2)*dx))
 
dx*dx/(sqrt(1 - 16*x^2))
 
dx*dx/((sqrt(1 - 16*x)*2))
 
dx*dx/((sqrt(1 - 16*x))^2)
 
dx*dx/((sqrt(1 - 1*16)*x^2))
 
dx*dx/(sqrt(1) - 16*x^2)
 
dx*(1 - 16*x^2)*dx/(sqrt(x))

Integral of dx/sqrt(1-16x^2)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  0                      
  /                      
 |                       
 |          1            
 |  1*--------------*1 dx
 |       ___________     
 |      /         2      
 |    \/  1 - 16*x       
 |                       
/                        
1/4
∫1401⋅1−16x2+1⋅1 dx\int\limits_{\frac{1}{4}}^{0} 1 \cdot \frac{1}{\sqrt{- 16 x^{2} + 1}} \cdot 1\, dx
Simplify
Detail solution

    TrigSubstitutionRule(theta=_theta, func=sin(_theta)/4, rewritten=1/4, substep=ConstantRule(constant=1/4, context=1/4, symbol=_theta), restriction=(x > -1/4) & (x < 1/4), context=1*1/sqrt(1 - 16*x**2), symbol=x)

  1. Now simplify:

    {asin⁡(4x)4for x>−14∧x<14NaNotherwise\begin{cases} \frac{\operatorname{asin}{\left(4 x \right)}}{4} & \text{for}\: x > - \frac{1}{4} \wedge x < \frac{1}{4} \\\text{NaN} & \text{otherwise} \end{cases}

  2. Add the constant of integration:

    {asin⁡(4x)4for x>−14∧x<14NaNotherwise+constant\begin{cases} \frac{\operatorname{asin}{\left(4 x \right)}}{4} & \text{for}\: x > - \frac{1}{4} \wedge x < \frac{1}{4} \\\text{NaN} & \text{otherwise} \end{cases}+ \mathrm{constant}

The answer is:

{asin⁡(4x)4for x>−14∧x<14NaNotherwise+constant\begin{cases} \frac{\operatorname{asin}{\left(4 x \right)}}{4} & \text{for}\: x > - \frac{1}{4} \wedge x < \frac{1}{4} \\\text{NaN} & \text{otherwise} \end{cases}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                                    
 |                                                                     
 |         1                   //asin(4*x)                            \
 | 1*--------------*1 dx = C + |<---------  for And(x > -1/4, x < 1/4)|
 |      ___________            \\    4                                /
 |     /         2                                                     
 |   \/  1 - 16*x                                                      
 |                                                                     
/
arcsin⁡(4 x)4{{\arcsin \left(4\,x\right)}\over{4}}
Simplify
The graph
0.0000.2500.0250.0500.0750.1000.1250.1500.1750.2000.2250100
Plot the graph f(x)
The answer [src] 
-pi 
----
 8
−π8-{{\pi}\over{8}} 
=
= 
-pi 
----
 8
−π8- \frac{\pi}{8}
Simplify
Numerical answer [src] 
-0.392699081604947
-0.392699081604947
The graph
Integral of dx/sqrt(1-16x^2)dx dx

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

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