Help Please

[elcatracho]

Hello, I had a question about doing this problem by hand....the Integral of
(Sec(x+pi/2) mutiplied by tan(x+pi/2) dx) I decided to make tan(x+pi/2)=u but when I move on and do Du, the numbers don't seem to match up. Is this problem able to be done by hand in a calc one class? If so how? thanks

 

[pka]

The answer is simply \(\displaystyle \L
\sec (x + \pi /2) + C\)

 

[galactus]

\(\displaystyle \L\\sec(x+\frac{{\pi}}{2})=\frac{-1}{sin(x)}\)

\(\displaystyle \L\\tan(x+\frac{{\pi}}{2})=\frac{-1}{tan(x)}\)

\(\displaystyle \L\\\frac{-1}{sin(x)}\frac{-1}{tan(x)}=\frac{cos(x)}{sin^{2}(x)}\)

\(\displaystyle \L\\\int{\frac{cos(x)}{sin^{2}(x)}}dx\)

Let u=sin(x), du=cos(x)dx

\(\displaystyle \L\\\int{\frac{du}{u^{2}}}\)

\(\displaystyle \L\\\frac{-1}{u}\)

Resub:

\(\displaystyle \L\\=\frac{-1}{sin(x)}\)