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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x*2^(-x)
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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 y^(-2/3)
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Identical expressions
- two /((two x+ two)^2+ three)
- 2 divide by ((2x plus 2) squared plus 3)
- two divide by ((two x plus two) squared plus three)
- 2/((2x+2)2+3)
- 2/2x+22+3
- 2/((2x+2)²+3)
- 2/((2x+2) to the power of 2+3)
- 2/2x+2^2+3
- 2 divide by ((2x+2)^2+3)
- 2/((2x+2)^2+3)dx
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Similar expressions
- 2/((2x-2)^2+3)
- 2/((2x+2)^2-3)
Integral of 2/((2x+2)^2+3) dx
The solution
You have entered
[src]
1 / | | 2 | -------------- dx | 2 | (2*x + 2) + 3 | / 0
$$\int\limits_{0}^{1} \frac{2}{\left(2 x + 2\right)^{2} + 3}\, dx$$
Integral(2/((2*x + 2)^2 + 3), (x, 0, 1))
The answer (Indefinite)
[src]
/ ___ \ / ___ |2*\/ 3 *(1 + x)| | \/ 3 *atan|---------------| | 2 \ 3 / | -------------- dx = C + --------------------------- | 2 3 | (2*x + 2) + 3 | /
$${{\arctan \left({{8\,x+8}\over{4\,\sqrt{3}}}\right)}\over{\sqrt{3}
}}$$
The graph
The answer
[src]
/ ___\ / ___\
___ |2*\/ 3 | ___ |4*\/ 3 |
\/ 3 *atan|-------| \/ 3 *atan|-------|
\ 3 / \ 3 /
- ------------------- + -------------------
3 3
$$2\,\left({{\arctan \left({{4}\over{\sqrt{3}}}\right)}\over{2\,
\sqrt{3}}}-{{\arctan \left({{2}\over{\sqrt{3}}}\right)}\over{2\,
\sqrt{3}}}\right)$$
=
=
/ ___\ / ___\
___ |2*\/ 3 | ___ |4*\/ 3 |
\/ 3 *atan|-------| \/ 3 *atan|-------|
\ 3 / \ 3 /
- ------------------- + -------------------
3 3
$$- \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{3} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3}}{3} \right)}}{3}$$
The graph
Use the examples entering the upper and lower limits of integration.