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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/sqrt(4-x^2)
- Integral of √((1-x)/(1+x))
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Integral of exp(7*x)*sin(x)
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Integral of 1/(x^2+2*x)
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Identical expressions
- one /(sqrt(three)(x^ three - one))
- 1 divide by ( square root of (3)(x cubed minus 1))
- one divide by ( square root of (three)(x to the power of three minus one))
- 1/(√(3)(x^3-1))
- 1/(sqrt(3)(x3-1))
- 1/sqrt3x3-1
- 1/(sqrt(3)(x³-1))
- 1/(sqrt(3)(x to the power of 3-1))
- 1/sqrt3x^3-1
- 1 divide by (sqrt(3)(x^3-1))
- 1/(sqrt(3)(x^3-1))dx
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Similar expressions
- 1/(sqrt(3)(x^3+1))
Integral of 1/(sqrt(3)(x^3-1)) dx
The solution
You have entered
[src]
1 / | | 1 | 1*-------------- dx | ___ / 3 \ | \/ 3 *\x - 1/ | / 0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{\sqrt{3} \left(x^{3} - 1\right)}\, dx$$
Integral(1/(sqrt(3)*(x^3 - 1*1)), (x, 0, 1))
The answer (Indefinite)
[src]
/ / 2\ / ___ \\ / ___ |log\1 + x + x / ___ |2*\/ 3 *(1/2 + x)|| | \/ 3 *|--------------- + \/ 3 *atan|-----------------|| ___ | 1 \ 2 \ 3 // \/ 3 *log(-1 + x) | 1*-------------- dx = C - ------------------------------------------------------- + ----------------- | ___ / 3 \ 9 9 | \/ 3 *\x - 1/ | /
$$\int 1 \cdot \frac{1}{\sqrt{3} \left(x^{3} - 1\right)}\, dx = C - \frac{\sqrt{3} \left(\frac{\log{\left(x^{2} + x + 1 \right)}}{2} + \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x + \frac{1}{2}\right)}{3} \right)}\right)}{9} + \frac{\sqrt{3} \log{\left(x - 1 \right)}}{9}$$
The answer
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/ ___ \
___ | pi*\/ 3 pi*I|
-oo - \/ 3 *|- -------- + ----|
\ 54 9 /
$$-\infty - \sqrt{3} \left(- \frac{\sqrt{3} \pi}{54} + \frac{i \pi}{9}\right)$$
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/ ___ \
___ | pi*\/ 3 pi*I|
-oo - \/ 3 *|- -------- + ----|
\ 54 9 /
$$-\infty - \sqrt{3} \left(- \frac{\sqrt{3} \pi}{54} + \frac{i \pi}{9}\right)$$
Use the examples entering the upper and lower limits of integration.