Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
- Integral of log(sin(x))
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Integral of cos(3x^2)
- Integral of cos^5(2t)sin^2(2t)dt
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Integral of xcosx/sin^2x
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Identical expressions
- cos(3x^ two)
- co sinus of e of (3x squared )
- co sinus of e of (3x to the power of two)
- cos(3x2)
- cos3x2
- cos(3x²)
- cos(3x to the power of 2)
- cos3x^2
- cos(3x^2)dx
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Similar expressions
- ((1/(cos3x)^2))-(1/sqrt(9x^2-4))
- x+(arccos3x)^2/sqrt(1-9x^2)
- cos(2x)^2*cos(3x)^2
- ((x+(arccos(3x))^2))/sqrt(1+9x^2)
Integral of cos(3x^2) dx
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
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Add the constant of integration:
FresnelCRule(a=3, b=0, c=0, context=cos(3*x**2), symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ ___\
___ ____ |x*\/ 6 |
/ \/ 6 *\/ pi *C|-------|
| | ____|
| / 2\ \ \/ pi /
| cos\3*x / dx = C + -----------------------
| 6
/
$$\int \cos{\left(3 x^{2} \right)}\, dx = C + \frac{\sqrt{6} \sqrt{\pi} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right)}{6}$$
The graph
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))
The graph
Use the examples entering the upper and lower limits of integration.