интегралы:
[tex]1) \int{\frac{1}{\sqrt[3]{x}+1}}\, dx \\ 2) \ind{\frac{2x-\sqrt{arcsin(x)}}{\sqrt{1-x^{2}}}}\, dx[/tex]
∫dx/ (∛x +1)= замена :∛х=t, x=t³, dx=3t²dt =3∫t²dt / (t+1)=3∫(t-1+ 1/(t+1)) *dt= 3(t²/2-t+ln|t+1))+C=3/2*(∛x)²-3∛x+ln|∛x+1|+C
2)...=∫2x*dx/√(1-x²) +∫√arcsinx*d(arcsinx) =-∫d(1-x²) / (1-x²) +(arcsin²x)/2= ln|1-x²|+(arcsin²x)/2+
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∫dx/ (∛x +1)= замена :∛х=t, x=t³, dx=3t²dt =3∫t²dt / (t+1)=3∫(t-1+ 1/(t+1)) *dt= 3(t²/2-t+ln|t+1))+C=3/2*(∛x)²-3∛x+ln|∛x+1|+C
2)...=∫2x*dx/√(1-x²) +∫√arcsinx*d(arcsinx) =-∫d(1-x²) / (1-x²) +(arcsin²x)/2= ln|1-x²|+(arcsin²x)/2+