The problem is:
But as u can see, answers dont ask me to solve it, so i sure that, there`re another way to get the answer
Improper integral or should i solve it?
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improper-integrals
1 Answers
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Start by noticing that as $x\to\infty$,
$$\frac{\sqrt x+\sqrt[3]{\sin x}}{x^{5/3}+x\cos x}\sim x^{-7/6}$$
So it converges as $x\to\infty$ by p-series. It should then be obvious that it must be positive, since the integrand is positive over the values, so...
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1@МузаффарШакаров No, I wouldn't compute $-6/x^{1/6}$ from $0$ to infinity. I wouldn't compute anything at all. Instead, the p-series says that$$\int_1^\infty\frac1{x^p}\ dx$$converges if $p>1$. That is true here. – 2017-01-07