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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of exp(7*x)*sin(x)
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Integral of cos^4(2x)
- Integral of e^(-x)/x
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Integral of cos(x)*exp(x)
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Identical expressions
- sin(ln^ two (x))/x
- sinus of (ln squared (x)) divide by x
- sinus of (ln to the power of two (x)) divide by x
- sin(ln2(x))/x
- sinln2x/x
- sin(ln²(x))/x
- sin(ln to the power of 2(x))/x
- sinln^2x/x
- sin(ln^2(x)) divide by x
- sin(ln^2(x))/xdx
Integral of sin(ln^2(x))/x dx
The solution
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[src]
1 / | | / 2 \ | sin\log (x)/ | ------------ dx | x | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(\log{\left(x \right)}^{2} \right)}}{x}\, dx$$
Integral(sin(log(x)^2)/x, (x, 0, 1))
The answer (Indefinite)
[src]
/ / | | | / 2 \ | / 2 \ | sin\log (x)/ | sin\log (x)/ | ------------ dx = C + | ------------ dx | x | x | | / /
$$\int \frac{\sin{\left(\log{\left(x \right)}^{2} \right)}}{x}\, dx = C + \int \frac{\sin{\left(\log{\left(x \right)}^{2} \right)}}{x}\, dx$$
The answer
[src]
1 / | | / 2 \ | sin\log (x)/ | ------------ dx | x | / 0
$$-\lim_{x\downarrow 0}{{{\sqrt{\pi}\,\left(\sqrt{2}\,i+\sqrt{2}
\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\log x}\over{2}}\right)}\over{16}}+{{\sqrt{\pi}\,\left(\sqrt{2}\,i-
\sqrt{2}\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i-\sqrt{2}
\right)\,\log x}\over{2}}\right)}\over{16}}+{{\sqrt{\pi}\,\left(
\sqrt{2}-\sqrt{2}\,i\right)\,\mathrm{erf}\left(\sqrt{-i}\,\log x
\right)}\over{16}}+{{\sqrt{\pi}\,\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\,\log x\right)
}\over{16}}}$$
=
=
1 / | | / 2 \ | sin\log (x)/ | ------------ dx | x | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(\log{\left(x \right)}^{2} \right)}}{x}\, dx$$
Use the examples entering the upper and lower limits of integration.