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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of tan^3(x)dx
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Integral of e^cos(x)*sin(x)
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Integral of dx/(2+x^2)
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Integral of e^x*sin(2x)
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Identical expressions
- arctan((2x+ one)/sqrt(three))
- arc tangent of ((2x plus 1) divide by square root of (3))
- arc tangent of ((2x plus one) divide by square root of (three))
- arctan((2x+1)/√(3))
- arctan2x+1/sqrt3
- arctan((2x+1) divide by sqrt(3))
- arctan((2x+1)/sqrt(3))dx
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Similar expressions
- arctan((2x-1)/sqrt(3))
Integral of arctan((2x+1)/sqrt(3)) dx
The solution
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[src]
1 / | | /2*x + 1\ | atan|-------| dx | | ___ | | \ \/ 3 / | / 0
$$\int\limits_{0}^{1} \operatorname{atan}{\left(\frac{2 x + 1}{\sqrt{3}} \right)}\, dx$$
Integral(atan((2*x + 1)/sqrt(3)), (x, 0, 1))
The answer (Indefinite)
[src]
/ / 2\ \
| | (2*x + 1) | |
| log|1 + ----------| ___ |
___ | \ 3 / \/ 3 /2*x + 1\|
/ \/ 3 *|- ------------------- + -----*(2*x + 1)*atan|-------||
| | 2 3 | ___ ||
| /2*x + 1\ \ \ \/ 3 //
| atan|-------| dx = C + -------------------------------------------------------------
| | ___ | 2
| \ \/ 3 /
|
/
$$\int \operatorname{atan}{\left(\frac{2 x + 1}{\sqrt{3}} \right)}\, dx = C + \frac{\sqrt{3} \left(\frac{\sqrt{3}}{3} \left(2 x + 1\right) \operatorname{atan}{\left(\frac{2 x + 1}{\sqrt{3}} \right)} - \frac{\log{\left(\frac{\left(2 x + 1\right)^{2}}{3} + 1 \right)}}{2}\right)}{2}$$
The graph
The answer
[src]
___ 5*pi \/ 3 *log(3) ---- - ------------ 12 4
$$- \frac{\sqrt{3} \log{\left(3 \right)}}{4} + \frac{5 \pi}{12}$$
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=
___ 5*pi \/ 3 *log(3) ---- - ------------ 12 4
$$- \frac{\sqrt{3} \log{\left(3 \right)}}{4} + \frac{5 \pi}{12}$$
5*pi/12 - sqrt(3)*log(3)/4
Use the examples entering the upper and lower limits of integration.