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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of cosx
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Integral of (1/x^2)dx
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Integral of x*cos(x/2)
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Integral of -x^3
- Graphing y =:
- x^(1/2)lnx
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Identical expressions
- x^(one / two)lnx
- x to the power of (1 divide by 2)lnx
- x to the power of (one divide by two)lnx
- x(1/2)lnx
- x1/2lnx
- x^1/2lnx
- x^(1 divide by 2)lnx
- x^(1/2)lnxdx
Integral of x^(1/2)lnx dx
The solution
You have entered
[src]
1 / | | ___ | \/ x *log(x) dx | / 0
$$\int\limits_{0}^{1} \sqrt{x} \log{\left(x \right)}\, dx$$
Integral(sqrt(x)*log(x), (x, 0, 1))
The answer (Indefinite)
[src]
/ | 3/2 3/2 | ___ 4*x 2*x *log(x) | \/ x *log(x) dx = C - ------ + ------------- | 9 3 /
$$4\,\left({{x^{{{3}\over{2}}}\,\log x}\over{6}}-{{x^{{{3}\over{2}}}
}\over{9}}\right)$$
The answer
[src]
1 / | | / ___ /1 \ | | 2*\/ x *log(x) for And|- < 1, x < 1| | | \x / | | | | ___ /1 \ | | \/ x *log(x) for Or|- < 1, x < 1| | | \x / | < dx | | __0, 3 /5/2, 5/2, 1 | \ | |3*/__ | | x| | | \_|3, 3 \ 3/2, 3/2, 0 | / __0, 3 /3/2, 5/2, 1 | \ __2, 1 / 0 5/2, 5/2 | \ | |---------------------------------------- + /__ | | x| /__ | | x| | | 2 \_|3, 3 \ 3/2, 3/2, 0 | / \_|3, 3 \3/2, 3/2 0 | / | |--------------------------------------------------------------------------------- - -------------------------------- otherwise | \ x x | / 0
$$-{{4}\over{9}}$$
=
=
1 / | | / ___ /1 \ | | 2*\/ x *log(x) for And|- < 1, x < 1| | | \x / | | | | ___ /1 \ | | \/ x *log(x) for Or|- < 1, x < 1| | | \x / | < dx | | __0, 3 /5/2, 5/2, 1 | \ | |3*/__ | | x| | | \_|3, 3 \ 3/2, 3/2, 0 | / __0, 3 /3/2, 5/2, 1 | \ __2, 1 / 0 5/2, 5/2 | \ | |---------------------------------------- + /__ | | x| /__ | | x| | | 2 \_|3, 3 \ 3/2, 3/2, 0 | / \_|3, 3 \3/2, 3/2 0 | / | |--------------------------------------------------------------------------------- - -------------------------------- otherwise | \ x x | / 0
$$\int\limits_{0}^{1} \begin{cases} 2 \sqrt{x} \log{\left(x \right)} & \text{for}\: \frac{1}{x} < 1 \wedge x < 1 \\\sqrt{x} \log{\left(x \right)} & \text{for}\: \frac{1}{x} < 1 \vee x < 1 \\\frac{{G_{3, 3}^{0, 3}\left(\begin{matrix} \frac{3}{2}, \frac{5}{2}, 1 & \\ & \frac{3}{2}, \frac{3}{2}, 0 \end{matrix} \middle| {x} \right)} + \frac{3 {G_{3, 3}^{0, 3}\left(\begin{matrix} \frac{5}{2}, \frac{5}{2}, 1 & \\ & \frac{3}{2}, \frac{3}{2}, 0 \end{matrix} \middle| {x} \right)}}{2}}{x} - \frac{{G_{3, 3}^{2, 1}\left(\begin{matrix} 0 & \frac{5}{2}, \frac{5}{2} \\\frac{3}{2}, \frac{3}{2} & 0 \end{matrix} \middle| {x} \right)}}{x} & \text{otherwise} \end{cases}\, dx$$
Use the examples entering the upper and lower limits of integration.