a) Calcule as integrais dadas abaixo e verifique suas respostas usando derivação: 1. ∫ xex/2 dx 2. ∫ (x2 + 2x) cosx dx 3. ∫ xe−x dx 4. ∫ p5 ln p dp...

1. ∫ xex/2 dx = 2xe^(x/2) - 4e^(x/2) + C Derivada: (2x + 4) e^(x/2) 2. ∫ (x^2 + 2x) cosx dx = (x^2 - 2) senx + 2xcosx + C Derivada: (x^2 + 4x - 2) cosx - 2(x^2 + 2) senx 3. ∫ xe^(-x) dx = -xe^(-x) - e^(-x) + C Derivada: (-x - 2) e^(-x) 4. ∫ p^5 ln(p) dp = (1/6) p^6 ln(p) - (1/36) p^6 + C Derivada: p^5 ln(p) - (5/36) p^5 + (1/6) p^6 5. ∫ arcsen(x) dx = x arcsen(x) + √(1 - x^2) + C Derivada: √(1 - x^2) 6. ∫ ln(x) dx = x ln(x) - x + C Derivada: ln(x) 7. ∫ √x ln(x) dx = (4/9) x^(3/2) ln(x) - (8/27) x^(3/2) + C Derivada: √x ln(x) - (2/3) √x 8. ∫ (x - 1) sec^2(x) dx = x tan(x) - ln|sec(x) + tan(x)| + C Derivada: (x - 2) sec^2(x) 9. ∫ x ln(3x) dx = (1/2) x^2 ln(3x) - (1/4) x^2 + C Derivada: x ln(3x) - (1/2) x 10. ∫ x^6 sen(x) dx = -x^6 cos(x) + 6x^5 sen(x) + 30x^4 cos(x) - 120x^3 sen(x) - 360x^2 cos(x) + 720x sen(x) + 720cos(x) + C Derivada: x^6 sen(x) + 6x^5 cos(x) - 30x^4 sen(x) - 120x^3 cos(x) + 360x^2 sen(x) + 720x cos(x) - 4320x^5