Question3. $\int \sec ^{5} x d x$
Solution:

Studdy Solution
Now solve for $\int \sec^5 x \, dx$ by rearranging:
$\int \sec^5 x \, dx = \sec^3 x \tan x - 3 \int \sec^3 x \, dx + 3 \int \sec^5 x \, dx$
Combine like terms and solve for $\int \sec^5 x \, dx$:
$-2 \int \sec^5 x \, dx = \sec^3 x \tan x - 3 \int \sec^3 x \, dx$
$\int \sec^5 x \, dx = -\frac{1}{2} \left( \sec^3 x \tan x - 3 \int \sec^3 x \, dx \right)$
The integral $\int \sec^5 x \, dx$ is expressed in terms of simpler integrals, which can be computed using standard techniques.