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How to use it?
- Integral of d{x}:
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Integral of sin^2(3x)
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Integral of x*e^(x^2)
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Integral of x*e^(2x)
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Integral of sin^3xcos^5x
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Identical expressions
- xlnx/(one +x²)²
- xlnx divide by (1 plus x²)²
- xlnx divide by (one plus x²)²
- xlnx/1+x²²
- xlnx divide by (1+x²)²
- xlnx/(1+x²)²dx
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Similar expressions
- xlnx/(1-x²)²
Integral of xlnx/(1+x²)² dx
The solution
You have entered
[src]
1 / | | x*log(x) | --------- dx | 2 | / 2\ | \1 + x / | / 0
$$\int\limits_{0}^{1} \frac{x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx$$
Integral((x*log(x))/(1 + x^2)^2, (x, 0, 1))
The answer (Indefinite)
[src]
/ 1 \ / log|1 + --| | | 2| | x*log(x) \ x / log(x) | --------- dx = C - ----------- - ---------- | 2 4 / 2\ | / 2\ 2*\1 + x / | \1 + x / | /
$$\int \frac{x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx = C - \frac{\log{\left(1 + \frac{1}{x^{2}} \right)}}{4} - \frac{\log{\left(x \right)}}{2 \left(x^{2} + 1\right)}$$
The graph
The answer
[src]
-log(2) -------- 4
$$- \frac{\log{\left(2 \right)}}{4}$$
=
=
-log(2) -------- 4
$$- \frac{\log{\left(2 \right)}}{4}$$
-log(2)/4
The graph
Use the examples entering the upper and lower limits of integration.