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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
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How to use it?
- Integral of d{x}:
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Integral of sqrt(x)*arctan(sqrt(x))
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Integral of cos(7x+2)
- Integral of xe^(xy)
- Integral of 2xlnx
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Identical expressions
- sqrt(x)*arctan(sqrt(x))
- square root of (x) multiply by arc tangent of ( square root of (x))
- √(x)*arctan(√(x))
- sqrt(x)arctan(sqrt(x))
- sqrtxarctansqrtx
- sqrt(x)*arctan(sqrt(x))dx
Integral of sqrt(x)*arctan(sqrt(x)) dx
The solution
You have entered
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1 / | | ___ / ___\ | \/ x *atan\\/ x / dx | / 0
$$\int\limits_{0}^{1} \sqrt{x} \operatorname{atan}{\left(\sqrt{x} \right)}\, dx$$
The answer (Indefinite)
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/ | 3/2 / ___\ | ___ / ___\ x log(1 + x) 2*x *atan\\/ x / | \/ x *atan\\/ x / dx = C - - + ---------- + ------------------ | 3 3 3 /
$$2\,\left({{\arctan \sqrt{x}\,x^{{{3}\over{2}}}}\over{3}}-{{{{x
}\over{2}}-{{\log \left(x+1\right)}\over{2}}}\over{3}}\right)$$
The graph
The answer
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1 log(2) pi - - + ------ + -- 3 3 6
$${{2\,\log 2+\pi-2}\over{6}}$$
=
=
1 log(2) pi - - + ------ + -- 3 3 6
$$- \frac{1}{3} + \frac{\log{\left(2 \right)}}{3} + \frac{\pi}{6}$$
The graph
Use the examples entering the upper and lower limits of integration.