Integral of (xsenx)/√x dx
The solution
The answer (Indefinite)
[src]
/ /
| |
| x*sin(x) | ___
| -------- dx = C + | \/ x *sin(x) dx
| ___ |
| \/ x /
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/
$$-{{16\,\sqrt{x}\,\cos x+\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2
}\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\sqrt{x}}\over{2}}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\mathrm{erf}\left({{\left(\sqrt{2}\,i-\sqrt{2}\right)\,\sqrt{x}
}\over{2}}\right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}
\left(\sqrt{-i}\,\sqrt{x}\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\,
\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\,\sqrt{x}\right)
\right)}\over{16}}$$
/ ___ \
___ ____ |\/ 2 |
5*\/ 2 *\/ pi *C|------|*Gamma(5/4)
| ____|
5*cos(1)*Gamma(5/4) \\/ pi /
- ------------------- + -----------------------------------
4*Gamma(9/4) 8*Gamma(9/4)
$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\,
\mathrm{erf}\left({{\sqrt{2}\,i+\sqrt{2}}\over{2}}\right)+\left(
\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}\left({{\sqrt{2}\,i-\sqrt{2
}}\over{2}}\right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}
\left(\sqrt{-i}\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\,
\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\right)\right)+16\,
\cos 1}\over{16}}$$
=
/ ___ \
___ ____ |\/ 2 |
5*\/ 2 *\/ pi *C|------|*Gamma(5/4)
| ____|
5*cos(1)*Gamma(5/4) \\/ pi /
- ------------------- + -----------------------------------
4*Gamma(9/4) 8*Gamma(9/4)
$$- \frac{5 \cos{\left(1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)}$$
Use the examples entering the upper and lower limits of integration.