Question

一个积分题

∫(a+x^2)^(3/2)dx
重点是怎么对a进行讨论，有解的

Answer 1

假设x=a^(1/2)tan(t)
那么原式=∫(a+x^2)^(3/2)dx=∫(a*(sec(t))^2)^(3/2)*d(a^(1/2)tan(t))=∫a^(3/2)*(sec(t))^3*d(a^(1/2)tan(t))
=∫a^2*(sec(t))^5*dt
=∫a^2*dt/(cos(t))^5
=∫a^2*d(sint)/(cos(t))^6
=a^2*∫d(sint)/(1-(sin(t))^3
=a^2*∫d(sint)/((1-(sin(t))^2)^3
=a^2*∫d(sint)/((1-(sin(t))^3*(1+(sin(t))^3)
=a^2*∫d(sint)/((1-(sin(t))^3*(1+(sin(t))^3)

Answer 2

25

Answer 3

少东西 无解

Answer 4

1

Answer 5

adx-dx+ax