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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sin²xcos²x
- Integral of ((1-x)/(1+x))^(1/2)
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Integral of x^2*e^2
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Integral of (x+1)e^(2x)
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Identical expressions
- x/(x^ two +4x+ three)
- x divide by (x squared plus 4x plus 3)
- x divide by (x to the power of two plus 4x plus three)
- x/(x2+4x+3)
- x/x2+4x+3
- x/(x²+4x+3)
- x/(x to the power of 2+4x+3)
- x/x^2+4x+3
- x divide by (x^2+4x+3)
- x/(x^2+4x+3)dx
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Similar expressions
- x/(x^2+4x-3)
- x/(x^2-4x+3)
Integral of x/(x^2+4x+3) dx
The solution
You have entered
[src]
1 / | | x | ------------ dx | 2 | x + 4*x + 3 | / 0
$$\int\limits_{0}^{1} \frac{x}{\left(x^{2} + 4 x\right) + 3}\, dx$$
Integral(x/(x^2 + 4*x + 3), (x, 0, 1))
The answer (Indefinite)
[src]
/ | / 2 \ | x log\3 + x + 4*x/ | ------------ dx = C + ----------------- - log(1 + x) + log(3 + x) | 2 2 | x + 4*x + 3 | /
$$\int \frac{x}{\left(x^{2} + 4 x\right) + 3}\, dx = C - \log{\left(x + 1 \right)} + \log{\left(x + 3 \right)} + \frac{\log{\left(x^{2} + 4 x + 3 \right)}}{2}$$
The graph
The answer
[src]
3*log(3) log(2) 3*log(4)
- -------- - ------ + --------
2 2 2
$$- \frac{3 \log{\left(3 \right)}}{2} - \frac{\log{\left(2 \right)}}{2} + \frac{3 \log{\left(4 \right)}}{2}$$
=
=
3*log(3) log(2) 3*log(4)
- -------- - ------ + --------
2 2 2
$$- \frac{3 \log{\left(3 \right)}}{2} - \frac{\log{\left(2 \right)}}{2} + \frac{3 \log{\left(4 \right)}}{2}$$
-3*log(3)/2 - log(2)/2 + 3*log(4)/2
The graph
Use the examples entering the upper and lower limits of integration.