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Integral of d{x}:
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Integral of sec^2(3x-1)+tan^2(3x-1)
Integral of sqrt(2x+4)
Identical expressions
sec^ two (3x- one)+tan^ two (3x- one)
sec squared (3x minus 1) plus tangent of squared (3x minus 1)
sec to the power of two (3x minus one) plus tangent of to the power of two (3x minus one)
sec2(3x-1)+tan2(3x-1)
sec23x-1+tan23x-1
sec²(3x-1)+tan²(3x-1)
sec to the power of 2(3x-1)+tan to the power of 2(3x-1)
sec^23x-1+tan^23x-1
sec^2(3x-1)+tan^2(3x-1)dx
Similar expressions
sec^2(3x-1)+tan^2(3x+1)
sec^2(3x+1)+tan^2(3x-1)
sec^2(3x-1)-tan^2(3x-1)

Solving integrals/ sec^2(3x-1)+tan^2(3x-1)

Integral of sec^2(3x-1)+tan^2(3x-1) dx

The solution

You have entered [src]

  1                                   
  /                                   
 |                                    
 |  /   2               2         \   
 |  \sec (3*x - 1) + tan (3*x - 1)/ dx
 |                                    
/                                     
0

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

Integral(sec(3*x - 1*1)^2 + tan(3*x - 1*1)^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int \tan^{2}{\left(3 x - 1 \right)}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int \sec^{2}{\left(3 x - 1 \right)}\, dx$
The result is: $\int \tan^{2}{\left(3 x - 1 \right)}\, dx + \int \sec^{2}{\left(3 x - 1 \right)}\, dx$
Now simplify:

$- x + \frac{\tan{\left(3 x - 1 \right)}}{3} + \int \sec^{2}{\left(3 x - 1 \right)}\, dx$
Add the constant of integration:

$- x + \frac{\tan{\left(3 x - 1 \right)}}{3} + \int \sec^{2}{\left(3 x - 1 \right)}\, dx+ \mathrm{constant}$

The answer is:

$- x + \frac{\tan{\left(3 x - 1 \right)}}{3} + \int \sec^{2}{\left(3 x - 1 \right)}\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           /                     /                
 |                                           |                     |                 
 | /   2               2         \           |    2                |    2            
 | \sec (3*x - 1) + tan (3*x - 1)/ dx = C +  | sec (3*x - 1) dx +  | tan (3*x - 1) dx
 |                                           |                     |                 
/                                           /                     /

$${{\tan \left(3\,x-1\right)-3\,x+1}\over{3}}+{{\tan \left(3\,x-1 \right)}\over{3}}$$

Simplify

The answer [src]

  1                                     
  /                                     
 |                                      
 |  /   2                2          \   
 |  \sec (-1 + 3*x) + tan (-1 + 3*x)/ dx
 |                                      
/                                       
0

$${{2\,\tan 2-2}\over{3}}+{{2\,\tan 1-1}\over{3}}$$

  1                                     
  /                                     
 |                                      
 |  /   2                2          \   
 |  \sec (-1 + 3*x) + tan (-1 + 3*x)/ dx
 |                                      
/                                       
0

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

Simplify

Numerical answer [src]

579.805844191396

579.805844191396

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

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Integral of sec^2(3x-1)+tan^2(3x-1) dx

Limits of integration:

The graph:

Piecewise:

The solution