Integration by Parts and Arclength

Back again! This time I have five problems that I have completed that, if anyone would be so kind, I would like to have looked over and corrected if they are wrong. Thank you very very much in advance!

**Problem 1.** dx

**My Solution**

u = ln(x), du = dx, dx = x du

du = du = ln(u) + C = = ln[ln( )] - ln[ln(e)] = ln[ln( )] - 0 = ln[ln( )]

**Problem 2. ** xsin4x dx

My Solution

u = x, du = dx, dv = sin4x, v = cos4x

dx = dx = = =

**Problem 3.** dx

**My Solution**

u = 4 + 9 , du = 18x dx, dx = \frac{1}{18}x du

du = du = du = =

**Problem 4.** dx

**My Solution**

dx = dx = dx = =

**Problem 5.** Calculate the length along the curve x = , y = ,

**My Solution** (Not so sure about this one.)

= , =

L = dt = dt = dt = dt = cos(t)sin(t) dt

u = cos(t), du = -sin(t) dt, dt = du

du = u du = = = -[0 - ] =

Once again, thank you very much in advance.