Question

i can't integrate (1+sec x)^3 dx

Answer 1

Expand out the cube thing,\[\large \int\limits(1+\sec x)^3\;dx\quad=\quad\int\limits(1+3\sec x+3\sec^2x+\sec^3x)\;dx\]

Answer 2

Integrate term by term.
They second and 4th term might be a little tricky.
The last one requires the Reduction Formula for Secant I believe.

Answer 3

yeah the problem is i already have an answer but i can't know if it's right or wrong cause the answer key is saying a different answer but the answer key have mistakes sometimes

Answer 4

So just be extra careful on the last term:
Let \(\Large \int\limits \sec^3x\;dx\quad=\quad I_3\)

Using the secant reduction formula:\[\Large I_3\quad=\quad \frac{1}{2}\sec x \tan x +\frac{1}{2}I_{1}\]\[\Large=\quad \frac{1}{2}\sec x \tan x+\frac{1}{2}\ln|\sec x +\tan x|\]

Answer 5

That's what integrating sec^3x should give us.

Answer 6

thanks that is exactly what i wanted