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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of (xsenx)/√x
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Integral of (8x^3+1)
- Integral of sqrt(x^3-2x^2+x)
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Integral of e^(5x)×sin3x
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Identical expressions
- (xsenx)/√x
- (xsenx) divide by √x
- xsenx/√x
- (xsenx)/√xdx
Integral of (xsenx)/√x dx
The solution
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1 / | | x*sin(x) | -------- dx | ___ | \/ x | / 0
$$\int\limits_{0}^{1} \frac{x \sin{\left(x \right)}}{\sqrt{x}}\, dx$$
Integral(x*sin(x)/(sqrt(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ / | | | x*sin(x) | ___ | -------- dx = C + | \/ x *sin(x) dx | ___ | | \/ x / | /
$$-{{16\,\sqrt{x}\,\cos x+\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2
}\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\sqrt{x}}\over{2}}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\mathrm{erf}\left({{\left(\sqrt{2}\,i-\sqrt{2}\right)\,\sqrt{x}
}\over{2}}\right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}
\left(\sqrt{-i}\,\sqrt{x}\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\,
\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\,\sqrt{x}\right)
\right)}\over{16}}$$
The graph
The answer
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/ ___ \
___ ____ |\/ 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)
$$- \frac{5 \cos{\left(1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)}$$
The graph
Use the examples entering the upper and lower limits of integration.