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cos(3x^2)
Solving integrals/ cos(3x^2)

Integral of cos(3x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |     /   2\   
 |  cos\3*x / dx
 |              
/               
0
$$\int\limits_{0}^{1} \cos{\left(3 x^{2} \right)}\, dx$$ 
Integral(cos(3*x^2), (x, 0, 1))
Detail solution

    FresnelCRule(a=3, b=0, c=0, context=cos(3*x**2), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
                                    /    ___\
                        ___   ____  |x*\/ 6 |
  /                   \/ 6 *\/ pi *C|-------|
 |                                  |   ____|
 |    /   2\                        \ \/ pi /
 | cos\3*x / dx = C + -----------------------
 |                               6           
/
$$\int \cos{\left(3 x^{2} \right)}\, dx = C + \frac{\sqrt{6} \sqrt{\pi} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right)}{6}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
              /  ___ \           
  ___   ____  |\/ 6  |           
\/ 6 *\/ pi *C|------|*Gamma(1/4)
              |  ____|           
              \\/ pi /           
---------------------------------
          24*Gamma(5/4)
$$\frac{\sqrt{6} \sqrt{\pi} C\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{24 \Gamma\left(\frac{5}{4}\right)}$$ 
=
= 
              /  ___ \           
  ___   ____  |\/ 6  |           
\/ 6 *\/ pi *C|------|*Gamma(1/4)
              |  ____|           
              \\/ pi /           
---------------------------------
          24*Gamma(5/4)
$$\frac{\sqrt{6} \sqrt{\pi} C\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{24 \Gamma\left(\frac{5}{4}\right)}$$ 
sqrt(6)*sqrt(pi)*fresnelc(sqrt(6)/sqrt(pi))*gamma(1/4)/(24*gamma(5/4))
Numerical answer [src] 
0.405955013881273
0.405955013881273
The graph
Integral of cos(3x^2) dx

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

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