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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of x^3*e^(x^4)
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Integral of x*e^(4*x)
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Integral of 1/(4+x^2)
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Integral of x/sqrt(1+x^2)
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Identical expressions
- arctgx^ three
- arctgx cubed
- arctgx to the power of three
- arctgx3
- arctgx³
- arctgx to the power of 3
- arctgx^3dx
Integral of arctgx^3 dx
The solution
You have entered
[src]
1 / | | 3 | acot (x) dx | / 0
$$\int\limits_{0}^{1} \operatorname{acot}^{3}{\left(x \right)}\, dx$$
The answer (Indefinite)
[src]
$${{32\,\left(3\,\int {{{\arctan \left({{1}\over{x}}\right)\,x^2\,
\left(\log \left(x^2+1\right)\right)^2}\over{32\,x^2+32}}}{\;dx}-3\,
\int {{{x\,\left(\log \left(x^2+1\right)\right)^2}\over{32\,x^2+32}}
}{\;dx}+3\,\int {{{\arctan \left({{1}\over{x}}\right)\,\left(\log
\left(x^2+1\right)\right)^2}\over{32\,x^2+32}}}{\;dx}+12\,\int {{{
\arctan \left({{1}\over{x}}\right)\,x^2\,\log \left(x^2+1\right)
}\over{32\,x^2+32}}}{\;dx}+28\,\int {{{\arctan ^3\left({{1}\over{x}}
\right)\,x^2}\over{32\,x^2+32}}}{\;dx}+12\,\int {{{\arctan ^2\left(
{{1}\over{x}}\right)\,x}\over{32\,x^2+32}}}{\;dx}-28\,\left({{3\,
\left(-{{\arctan ^4x}\over{12}}-{{\arctan \left({{1}\over{x}}\right)
\,\arctan ^3x}\over{3}}\right)}\over{32}}-{{3\,\arctan ^2\left({{1
}\over{x}}\right)\,\arctan ^2x}\over{64}}\right)+{{7\,\arctan ^3
\left({{1}\over{x}}\right)\,\arctan x}\over{8}}\right)-3\,
{\rm atan2}\left(1 , x\right)\,x\,\left(\log \left(x^2+1\right)
\right)^2+4\,{\rm atan2}\left(1 , x\right)^3\,x}\over{32}}$$
The answer
[src]
1 / | | 3 | acot (x) dx | / 0
$$\int_{0}^{1}{\left({\rm arccot}\; x\right)^3\;dx}$$
=
=
1 / | | 3 | acot (x) dx | / 0
$$\int\limits_{0}^{1} \operatorname{acot}^{3}{\left(x \right)}\, dx$$
Use the examples entering the upper and lower limits of integration.