Resolva as integrais abaixo. a) ∫ dttt 2 cos b) ∫ + + dx x2x 1x 2 c) ∫ + dx x9 x 2 3 d) ∫ dx xsen xcos 4 3

a) ∫ dt/(t^2 cos) = 1/2 ∫ sec(u) du = 1/2 ln|sec(u) + tan(u)| + C, onde u = ln|t| Resposta: 1/2 ln|sec(ln|t|) + tan(ln|t|)| + C b) ∫ dx/(x^2 * (2x+1)) = 1/2 ∫ (1/x - 2/(2x+1)) dx = 1/2 ln|x| - ln|2x+1| + C Resposta: 1/2 ln|x| - ln|2x+1| + C c) ∫ dx/(x^9 * sqrt(x^2 + 3)) = 1/3 ∫ (x^(-8) * (x^2 + 3)^(-1/2)) d(x^2 + 3) = -1/3 (x^(-8) * sqrt(x^2 + 3)) + 1/3 ∫ (4x^(-10) * sqrt(x^2 + 3)) dx Resposta: -1/3 (x^(-8) * sqrt(x^2 + 3)) + 2/15 (x^(-6) * sqrt(x^2 + 3)) + C d) ∫ dx/(x * sen^(4/3)(x) * cos^(2/3)(x)) = 3/2 ∫ sec^(2/3)(x) d(sec^(1/3)(x)) = 3/2 (3/5 sec^(5/3)(x)) + C Resposta: 9/10 sec^(5/3)(x) + C