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Solving integrals/ (x^(1÷2))tan^2(x)

Integral of (x^(1÷2))tan^2(x) dx

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∫01xtan⁡2(x) dx\int\limits_{0}^{1} \sqrt{x} \tan^{2}{\left(x \right)}\, dx 
Integral(sqrt(x)*tan(x)^2, (x, 0, 1))
The answer (Indefinite) [src]
−(−3 sin⁡2(4 x)−12 sin⁡(2 x) sin⁡(4 x)−3 cos⁡2(4 x)+(−12 cos⁡(2 x)−6) cos⁡(4 x)−12 sin⁡2(2 x)−12 cos⁡2(2 x)−12 cos⁡(2 x)−3) ∫x ((6 sin⁡(4 x)+8 x cos⁡(4 x)+3 sin⁡(2 x)) sin⁡(6 x)+(−8 x sin⁡(4 x)+6 cos⁡(4 x)+3 cos⁡(2 x)−3) cos⁡(6 x)+18 sin⁡2(4 x)+(27 sin⁡(2 x)−24 x cos⁡(2 x)−8 x) sin⁡(4 x)+18 cos⁡2(4 x)+(24 x sin⁡(2 x)+27 cos⁡(2 x)−3) cos⁡(4 x)+9 sin⁡2(2 x)+9 cos⁡2(2 x)−6 cos⁡(2 x)−3)3 sin⁡2(6 x)+(18 sin⁡(4 x)+18 sin⁡(2 x)) sin⁡(6 x)+3 cos⁡2(6 x)+(18 cos⁡(4 x)+18 cos⁡(2 x)+6) cos⁡(6 x)+27 sin⁡2(4 x)+54 sin⁡(2 x) sin⁡(4 x)+27 cos⁡2(4 x)+(54 cos⁡(2 x)+18) cos⁡(4 x)+27 sin⁡2(2 x)+27 cos⁡2(2 x)+18 cos⁡(2 x)+3  dx+x (2 x sin⁡2(4 x)+4 x sin⁡(2 x) sin⁡(4 x)+2 x cos⁡2(4 x)+(4 x cos⁡(2 x)+2 x) cos⁡(4 x))3 sin⁡2(4 x)+12 sin⁡(2 x) sin⁡(4 x)+3 cos⁡2(4 x)+(12 cos⁡(2 x)+6) cos⁡(4 x)+12 sin⁡2(2 x)+12 cos⁡2(2 x)+12 cos⁡(2 x)+3-{{\left(-3\,\sin ^2\left(4\,x\right)-12\,\sin \left(2\,x\right)\, \sin \left(4\,x\right)-3\,\cos ^2\left(4\,x\right)+\left(-12\,\cos \left(2\,x\right)-6\right)\,\cos \left(4\,x\right)-12\,\sin ^2\left( 2\,x\right)-12\,\cos ^2\left(2\,x\right)-12\,\cos \left(2\,x\right)- 3\right)\,\int {{{\sqrt{x}\,\left(\left(6\,\sin \left(4\,x\right)+8 \,x\,\cos \left(4\,x\right)+3\,\sin \left(2\,x\right)\right)\,\sin \left(6\,x\right)+\left(-8\,x\,\sin \left(4\,x\right)+6\,\cos \left( 4\,x\right)+3\,\cos \left(2\,x\right)-3\right)\,\cos \left(6\,x \right)+18\,\sin ^2\left(4\,x\right)+\left(27\,\sin \left(2\,x \right)-24\,x\,\cos \left(2\,x\right)-8\,x\right)\,\sin \left(4\,x \right)+18\,\cos ^2\left(4\,x\right)+\left(24\,x\,\sin \left(2\,x \right)+27\,\cos \left(2\,x\right)-3\right)\,\cos \left(4\,x\right)+ 9\,\sin ^2\left(2\,x\right)+9\,\cos ^2\left(2\,x\right)-6\,\cos \left(2\,x\right)-3\right)}\over{3\,\sin ^2\left(6\,x\right)+\left( 18\,\sin \left(4\,x\right)+18\,\sin \left(2\,x\right)\right)\,\sin \left(6\,x\right)+3\,\cos ^2\left(6\,x\right)+\left(18\,\cos \left(4 \,x\right)+18\,\cos \left(2\,x\right)+6\right)\,\cos \left(6\,x \right)+27\,\sin ^2\left(4\,x\right)+54\,\sin \left(2\,x\right)\, \sin \left(4\,x\right)+27\,\cos ^2\left(4\,x\right)+\left(54\,\cos \left(2\,x\right)+18\right)\,\cos \left(4\,x\right)+27\,\sin ^2 \left(2\,x\right)+27\,\cos ^2\left(2\,x\right)+18\,\cos \left(2\,x \right)+3}}}{\;dx}+\sqrt{x}\,\left(2\,x\,\sin ^2\left(4\,x\right)+4 \,x\,\sin \left(2\,x\right)\,\sin \left(4\,x\right)+2\,x\,\cos ^2 \left(4\,x\right)+\left(4\,x\,\cos \left(2\,x\right)+2\,x\right)\, \cos \left(4\,x\right)\right)}\over{3\,\sin ^2\left(4\,x\right)+12\, \sin \left(2\,x\right)\,\sin \left(4\,x\right)+3\,\cos ^2\left(4\,x \right)+\left(12\,\cos \left(2\,x\right)+6\right)\,\cos \left(4\,x \right)+12\,\sin ^2\left(2\,x\right)+12\,\cos ^2\left(2\,x\right)+12 \,\cos \left(2\,x\right)+3}}
Simplify
The answer [src] 
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∫01x tan⁡2x  dx\int_{0}^{1}{\sqrt{x}\,\tan ^2x\;dx} 
=
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∫01xtan⁡2(x) dx\int\limits_{0}^{1} \sqrt{x} \tan^{2}{\left(x \right)}\, dx
Упростить
Numerical answer [src] 
0.49232661339107
0.49232661339107

    Use the examples entering the upper and lower limits of integration.

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