∫(sinx + secx) / tanx dx

∫(sinx/tanx)dx + ∫(secx/tanx)dx

∫(cosx)dx + ∫(1/sinx)dx

sinx + ... not sure where to go from here. tried to go ∫(sinx/sinx^2)

1/2∫(sinx/1-cos2x)

u=1-cos2x du=2sinxdx dx=du/2sinx

1/2∫(sinx/2)(du/2sinx)

1/4∫(1/u)du

so... sinx + 1/4(ln|1-cos2x|)

but the back of the book says the answer is sinx + ln | cscx-cotx |

any ideas??? help!!!!!!!!!!!!!!!!!!!!!!!!!!!