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How to use it?
- Integral of d{x}:
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Integral of x^2/(1+x^3)
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Integral of x^2/sqrt(4-x^2)
- Integral of x^2/(x-1)
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Integral of (x^2)/(x+1)
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Identical expressions
- atan(x)/x^(one / three)
- arc tangent of gent of (x) divide by x to the power of (1 divide by 3)
- arc tangent of gent of (x) divide by x to the power of (one divide by three)
- atan(x)/x(1/3)
- atanx/x1/3
- atanx/x^1/3
- atan(x) divide by x^(1 divide by 3)
- atan(x)/x^(1/3)dx
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Similar expressions
- arctan(x)/x^(1/3)
- arctanx/x^(1/3)
Integral of atan(x)/x^(1/3) dx
The solution
You have entered
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-100 / | | atan(x) | ------- dx | 3 ___ | \/ x | / 0
$$\int\limits_{0}^{-100} \frac{\operatorname{atan}{\left(x \right)}}{\sqrt[3]{x}}\, dx$$
Integral(atan(x)/x^(1/3), (x, 0, -100))
The answer (Indefinite)
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/ | /3 ___\ / ___ 3 ___\ / ___ 3 ___\ ___ / 2/3 ___ 3 ___\ 2/3 ___ / 2/3 ___ 3 ___\ | atan(x) 3*atan\\/ x / 3*atan\\/ 3 + 2*\/ x / 3*atan\- \/ 3 + 2*\/ x / 3*\/ 3 *log\4 + 4*x - 4*\/ 3 *\/ x / 3*x *atan(x) 3*\/ 3 *log\4 + 4*x + 4*\/ 3 *\/ x / | ------- dx = C - ------------- - ----------------------- - ------------------------- - --------------------------------------- + -------------- + --------------------------------------- | 3 ___ 2 4 4 8 2 8 | \/ x | /
$$\int \frac{\operatorname{atan}{\left(x \right)}}{\sqrt[3]{x}}\, dx = C + \frac{3 x^{\frac{2}{3}} \operatorname{atan}{\left(x \right)}}{2} - \frac{3 \sqrt{3} \log{\left(4 x^{\frac{2}{3}} - 4 \sqrt{3} \sqrt[3]{x} + 4 \right)}}{8} + \frac{3 \sqrt{3} \log{\left(4 x^{\frac{2}{3}} + 4 \sqrt{3} \sqrt[3]{x} + 4 \right)}}{8} - \frac{3 \operatorname{atan}{\left(\sqrt[3]{x} \right)}}{2} - \frac{3 \operatorname{atan}{\left(2 \sqrt[3]{x} - \sqrt{3} \right)}}{4} - \frac{3 \operatorname{atan}{\left(2 \sqrt[3]{x} + \sqrt{3} \right)}}{4}$$
Numerical answer
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(23.3483049051421 - 40.4404503663158j)
(23.3483049051421 - 40.4404503663158j)
Use the examples entering the upper and lower limits of integration.