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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
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Integral of dx/(1+x^2)
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Integral of exp(y)
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Integral of -exp(-x)
- Integral of ln(x)/√x
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Identical expressions
- xln(2x²-2x+ one)
- xln(2x² minus 2x plus 1)
- xln(2x² minus 2x plus one)
- xln2x²-2x+1
- xln(2x²-2x+1)dx
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Similar expressions
- xln(2x²-2x-1)
- xln(2x²+2x+1)
Integral of xln(2x²-2x+1) dx
The solution
You have entered
[src]
1 / | | / 2 \ | x*log\2*x - 2*x + 1/ dx | / 0
$$\int\limits_{0}^{1} x \log{\left(\left(2 x^{2} - 2 x\right) + 1 \right)}\, dx$$
Integral(x*log(2*x^2 - 2*x + 1), (x, 0, 1))
The answer (Indefinite)
[src]
/ | 2 2 / 2 \ | / 2 \ atan(-1 + 2*x) x x x *log\2*x - 2*x + 1/ | x*log\2*x - 2*x + 1/ dx = C + -------------- - - - -- + ---------------------- | 2 2 2 2 /
$$\int x \log{\left(\left(2 x^{2} - 2 x\right) + 1 \right)}\, dx = C + \frac{x^{2} \log{\left(\left(2 x^{2} - 2 x\right) + 1 \right)}}{2} - \frac{x^{2}}{2} - \frac{x}{2} + \frac{\operatorname{atan}{\left(2 x - 1 \right)}}{2}$$
The graph
The answer
[src]
pi
-1 + --
4
$$-1 + \frac{\pi}{4}$$
=
=
pi
-1 + --
4
$$-1 + \frac{\pi}{4}$$
-1 + pi/4
The graph
Use the examples entering the upper and lower limits of integration.