Mister Exam

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cos(3x^ two + four)
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cos(3x2+4)
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cos3x^2+4
cos(3x^2+4)dx
Similar expressions
cos(3x^2-4)

Solving integrals/ cos(3x^2+4)

Integral of cos(3x^2+4) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |     /   2    \   
 |  cos\3*x  + 4/ dx
 |                  
/                   
0

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

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

Detail solution

FresnelCRule(a=3, b=0, c=4, context=cos(3*x**2 + 4), symbol=x)

Add the constant of integration:

$\frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right)\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right)\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

                                       /        /    ___\    /    ___\       \
                            ___   ____ |        |x*\/ 6 |    |x*\/ 6 |       |
  /                       \/ 6 *\/ pi *|cos(4)*C|-------| - S|-------|*sin(4)|
 |                                     |        |   ____|    |   ____|       |
 |    /   2    \                       \        \ \/ pi /    \ \/ pi /       /
 | cos\3*x  + 4/ dx = C + ----------------------------------------------------
 |                                                 6                          
/

$$\int \cos{\left(3 x^{2} + 4 \right)}\, dx = C + \frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right)\right)}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

             /        /  ___ \    /  ___ \       \
  ___   ____ |        |\/ 6  |    |\/ 6  |       |
\/ 6 *\/ pi *|cos(4)*C|------| - S|------|*sin(4)|
             |        |  ____|    |  ____|       |
             \        \\/ pi /    \\/ pi /       /
--------------------------------------------------
                        6

$$\frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right)\right)}{6}$$

             /        /  ___ \    /  ___ \       \
  ___   ____ |        |\/ 6  |    |\/ 6  |       |
\/ 6 *\/ pi *|cos(4)*C|------| - S|------|*sin(4)|
             |        |  ____|    |  ____|       |
             \        \\/ pi /    \\/ pi /       /
--------------------------------------------------
                        6

$$\frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right)\right)}{6}$$

sqrt(6)*sqrt(pi)*(cos(4)*fresnelc(sqrt(6)/sqrt(pi)) - fresnels(sqrt(6)/sqrt(pi))*sin(4))/6

Numerical answer [src]

0.124385348693692

0.124385348693692

The graph

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

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Identical expressions

Similar expressions

Integral of cos(3x^2+4) dx

Limits of integration:

The graph:

Piecewise:

The solution