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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sin(5x)
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Integral of x²+2x
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Integral of (x^2+2x)
- Integral of ln|secx+tanx|dx
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Identical expressions
- x/(cbrt(3x- one))
- x divide by ( cubic root of (3x minus 1))
- x divide by ( cubic root of (3x minus one))
- x/cbrt3x-1
- x divide by (cbrt(3x-1))
- x/(cbrt(3x-1))dx
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Similar expressions
- x/(cbrt(3x+1))
Integral of x/(cbrt(3x-1)) dx
The solution
You have entered
[src]
1 / | | x | ----------- dx | 3 _________ | \/ 3*x - 1 | / 0
$$\int\limits_{0}^{1} \frac{x}{\sqrt[3]{3 x - 1}}\, dx$$
Integral(x/((3*x - 1*1)^(1/3)), (x, 0, 1))
The answer (Indefinite)
[src]
/ | 2/3 5/3 | x (-1 + 3*x) (-1 + 3*x) | ----------- dx = C + ------------- + ------------- | 3 _________ 6 15 | \/ 3*x - 1 | /
$$\int \frac{x}{\sqrt[3]{3 x - 1}}\, dx = C + \frac{\left(3 x - 1\right)^{\frac{5}{3}}}{15} + \frac{\left(3 x - 1\right)^{\frac{2}{3}}}{6}$$
The graph
The answer
[src]
-pi*I ------ 3 2/3 e 3*2 ------- + ------ 10 10
$$\frac{3 \cdot 2^{\frac{2}{3}}}{10} + \frac{e^{- \frac{i \pi}{3}}}{10}$$
=
=
-pi*I ------ 3 2/3 e 3*2 ------- + ------ 10 10
$$\frac{3 \cdot 2^{\frac{2}{3}}}{10} + \frac{e^{- \frac{i \pi}{3}}}{10}$$
Numerical answer
[src]
(0.565753180979214 - 0.0770367074763296j)
(0.565753180979214 - 0.0770367074763296j)
The graph
Use the examples entering the upper and lower limits of integration.