Integral 3x (sinx/cos^4x) dx

[413]

can anybody help me with this problem
Evaluate :
integral 3x (sinx/cos^4x) dx

 

[courtrigrad]

Is it $$\int \frac{3x\sin x}{\cos^{4} x}$$?

Rewrite it as $$3\int x\tan x\ sec^{3} x$$ and use integration by parts

 

[413]

i know the equation for intergration by parts is
intergral u dv = uv -intergral v du

can u tell me which variable is which?...u, du, v, dv=?...there seems to have 3 different variable.

 

[courtrigrad]

Let $$u = x$$ and $$dv = \ tan x \sec^{3} x$$. You will then need to use integration by parts on $$dv$$ to get $$v$$.

 

[HallsofIvy]

I'm sure courtrigrad meant $u= x$ and $dv= tan x sec^3 xdx$ (with out the "x" in dv).

 

[courtrigrad]

yep, thanks catching that