Question

Using Substitution Rule, find:

1) ∫(sec^2(1/x))/x^2
2) ∫(sec^2)2Θ

Answer 1

\[\huge \int \frac{\sec^2 \left(\frac 1x \right)}{x^2} dx\]
let \[u = \frac 1x\]
\[du = -\frac 1{x^2}\]
so your integral becomes
\[\huge \implies -\int \sec^2 u du\]
does that help?

Answer 2

Yes, it does. Thank you! :)

Answer 3

welcome

Answer 4

for the second part
\[\huge ]int \sec^2 (2\theta) d\theta\]
let \[u = 2\theta\]
\[du = 2d \theta\]
so your integral becomes
\[\huge \implies \frac 12 \int \sec^2 u du\]

Answer 5

Thank you! x 10000000 :)

Answer 6

welcome