How do you integrate int x^3*sqrt(4+x^2) using integration by parts?

1 Answer
Jan 19, 2016

not by using integration by part

u = x^2+4
du = 2x

1/2int2x^3*sqrt(x^2+4) du

1/2intx^2*sqrt(u)du

x^2 = u-4

1/2int(u-4)*sqrt(u)du

expand

1/2intu*sqrt(u)-4sqrt(u)du

1/2intu^(3/2)-4sqrt(u)du

1/2[2/5u^(5/2)-8/3u^(3/2)]+C

[1/5u^(5/2)-4/3u^(3/2)]+C