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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(x+2)^2
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Integral of xarctanx
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Integral of e^(x^3)
- Integral of ln(x)/x^3
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Identical expressions
- sin(x^ two)dx
- sinus of (x squared )dx
- sinus of (x to the power of two)dx
- sin(x2)dx
- sinx2dx
- sin(x²)dx
- sin(x to the power of 2)dx
- sinx^2dx
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Similar expressions
- x*sinx^2dx
- x^3sinx^2dx
- xsinx^2dx
Integral of sin(x^2)dx dx
The solution
You have entered
[src]
1 / | | / 2\ | sin\x /*1 dx | / 0
$$\int\limits_{0}^{1} \sin{\left(x^{2} \right)} 1\, dx$$
Integral(sin(x^2)*1, (x, 0, 1))
Detail solution
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Add the constant of integration:
FresnelSRule(a=1, b=0, c=0, context=sin(x**2)*1, symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ ___\
___ ____ |x*\/ 2 |
/ \/ 2 *\/ pi *S|-------|
| | ____|
| / 2\ \ \/ pi /
| sin\x /*1 dx = C + -----------------------
| 2
/
$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}
\left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\,x}\over{2}}\right)+\left(
\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i-
\sqrt{2}\right)\,x}\over{2}}\right)+\left(\sqrt{2}-\sqrt{2}\,i
\right)\,\mathrm{erf}\left(\sqrt{-i}\,x\right)+\left(\sqrt{2}\,i+
\sqrt{2}\right)\,\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\,
x\right)\right)}\over{16}}$$
The graph
The answer
[src]
/ ___ \
___ ____ |\/ 2 |
3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
| ____|
\\/ pi /
-----------------------------------
8*Gamma(7/4)
$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}
\left({{\sqrt{2}\,i+\sqrt{2}}\over{2}}\right)+\left(\sqrt{2}\,i-
\sqrt{2}\right)\,\mathrm{erf}\left({{\sqrt{2}\,i-\sqrt{2}}\over{2}}
\right)+\left(\sqrt{2}-\sqrt{2}\,i\right)\,\mathrm{erf}\left(\sqrt{-
i}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}\left(
\left(-1\right)^{{{1}\over{4}}}\right)\right)}\over{16}}$$
=
=
/ ___ \
___ ____ |\/ 2 |
3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
| ____|
\\/ pi /
-----------------------------------
8*Gamma(7/4)
$$\frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}$$
The graph
Use the examples entering the upper and lower limits of integration.