Помогите решить интеграл. Заранее спасибо.
[tex] \int\limits {\frac{ x^{2} dx}{ \sqrt{2 x^{3}-5 } }} \, [/tex]
[tex] \int\limits {\frac{ x^{2} dx}{ \sqrt{2 x^{3}-5 } }} \, [/tex]
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= (1/6) Интеграл (2x³ -5) ^(-1/2) d(2x³ -5) =(1/6)* (2x³ -5) ^(-1/2+1)/(-1/2+1) ==(1/3)*√(2x³ -5) +C.
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Интеграл (2x³ -5) ^(-1/2) d(2x³ -5) p
2x³ -5=t
Интеграл t ^(-1/2) dt = t ^(-1/2+1)/(-1/2+1 =2t^(1/2) =2√t