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∫(π/4→π/3) x/sin?x dx

= ∫(π/4→π/3) xcsc?x dx

= ∫(π/4→π/3) x d(- cotx)

= - xcotx ∫(π/4→π/3) cotx dx

= - xcotx ∫(π/4→π/3) 1/sinx d(sinx)

= - xcotx ln(sinx) |(π/4→π/3)

= ( - π/3)cot(π/3) ln(sin(π/3)) - [(- π/4)cot(π/4) ln(sin(π/4))]

= (1/36)(9 - 4√3)π (1/2)ln(3/2) ≈ 0.383531

Mi respuesta es correcta, el cálculo es el siguiente.

/input/?i=int_28pi2F4295E28pi2F329 x2Fsin5E2x dx