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How to use it?
- Integral of d{x}:
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Integral of 1/(x^2+6x+11)
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Integral of cos(3x^2+4)
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Integral of arcsin(x)/(sqrt(1-x^2))
- Integral of xsiny
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Identical expressions
- cos(3x^ two + four)
- co sinus of e of (3x squared plus 4)
- co sinus of e of (3x to the power of two plus four)
- cos(3x2+4)
- cos3x2+4
- cos(3x²+4)
- cos(3x to the power of 2+4)
- cos3x^2+4
- cos(3x^2+4)dx
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Similar expressions
- cos(3x^2-4)
Integral of cos(3x^2+4) dx
The solution
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[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
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Add the constant of integration:
FresnelCRule(a=3, b=0, c=4, context=cos(3*x**2 + 4), symbol=x)
The answer is:
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
/
$$\int \cos{\left(3 x^{2} + 4 \right)}\, dx = C + \frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right)\right)}{6}$$
The graph
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
The graph
Use the examples entering the upper and lower limits of integration.