dead end intergral...please help

[roxstar1]

could someone please help me solve this?


integral (sec^2(5x)) dx


my work so far:

integral (tan^2(5x) + 1)(sec^2(5x)) dx

integral (tan^2(5x)sec^2(5x) dx + integral sec^2(5x) dx

? + tan(5x) + c

 

[ChaoticLlama]

you're thinking too hard.

What is the integral of sec²(u)?

once you answer that question, you will be close.

 

[roxstar1]

oops....I accidently wrote the question wrong...its supposed to be:

integral [sec^4(5x)] dx

 

[soroban]

Hello, roxstar1!

\(\displaystyle \L\int\)\(\displaystyle sec^{^4}(5x)\,dx\)

My work so far:

\(\displaystyle \L\;\;\int\)\(\displaystyle [\tan^2(5x) + 1]\,[\sec^2(5x)]\, dx\)

\(\displaystyle \L\;\;\int\)\(\displaystyle \tan^2(5x)\cdot\sec^2(5x)\,dx\;+\;\L\int\)\(\displaystyle \sec^2(5x)\,dx\;\;\) . . . good!

For the first integral, let \(\displaystyle u\,=\,\tan(5x)\)

BTW, the second is: \(\displaystyle \,\frac{1}{5}\tan(5x)\)