(1)x^3根号下(4-x^2)(2)根号下[(x^2-9)/x^2](1)-4/3(4-x^2)^(3/2)+1/5(4-x^2)^(5/2)+c(2)ln[x+根号下(x^2-9)]-(根号下x^2-9)/x+c

Question

(1)x^3根号下(4-x^2)
(2)根号下[(x^2-9)/x^2]
(1)-4/3(4-x^2)^(3/2)+1/5(4-x^2)^(5/2)+c
(2)ln[x+根号下(x^2-9)]-(根号下x^2-9)/x+c

Answer 1

(1)令u=4-x^2,du=-2xdx
∴=(-1/2)∫(4-u)√udu
=1/5*u^5/2-4/3*u^3/2+C
=(1/5)(4-x^2)^(5/2)-(4/3)(4-x^2)^3/2
(2)令x=3secu,dx=3secutanu
∴=∫(secu-cosu)du
=ln(tanu+secu)-sinu
=ln(x+√(x^2-9)]-√(x^2-9)/x