Question

Evaluate the integral. (Remember to use ln |u| where appropriate. Use C for the constant of integration.)

integral 5x sec x tan x dx

Answer 1

Integrate by parts:
\[\int 5x \sec x\tan x~dx=5\left[uv-\int v~du\right]\]
with
\[\begin{matrix}u=x&&&dv=\sec x\tan x~dx\\du=dx&&&v=\sec x\end{matrix}\]
\[5\left[x\sec x-\int \sec x~dx\right]\]