Question

Hello, I just wanted to verify if my work was good.

Calculate the following integral by parts:

∫ upper limit is 1/5 and lower limit is 1/10. of 10sin^-1 (5x)dx

so first I named the variables:

u = 10 sin^-1 (5x)
du = 50 / sqr(1-25x^2)

dv = dx
v = x

so we get:

= 10 sin^-1 (5x)(x) - ∫50x/(1-25x^2)
= 10 sin^-1 (5x)(x)|1/5, 1/10 -
∫50x/(1-25x^2) |1/5, 1/10

let w = 1-25x^2
dw = -50xdx

= 10 sin^-1 (5x)(x) + ∫ 1/sqr(w)dw
= 10 sin^-1 (5x)(x) + 2sqr(w) + C |1/5, 1/10

= 180 - (30 + 2sqr(0.75))

= 148.27

Thanks!