Solving the Integral: sec(x)^2 / 4+tan(x)^2

[whatlifeforme]

Homework Statement

solve the integral.

Homework Equations

integral (sec(x)^2 / 4+tan(x)^2)

The Attempt at a Solution

i tried replacing the numerator with the trig identity: tan(x)^2 + 1 -- but not sure what else to try.

 

[Saitama]

There is a very obvious substitution you can do here.

 

[Ferramentarius]

Consider the derivatives of trigonometric functions.

 

[whatlifeforme]

was the step i performed correct?

 

[SammyS]

was the step i performed correct?

No.

What is the derivative of tan(x) ?

 

[VertexOperator]

What is d/dx (tanx)?
Edit: or what sammy says :)

 

[jfgobin]

Also, be careful that an integral is not the same thing as an antiderivative.

 

[HallsofIvy]

The first thing I would do is replace sec²(x) with 1/cos²(x) and replace tan²(x) with sin²(x)/cos^2(x).

 

[iRaid]

The first thing I would do is replace sec²(x) with 1/cos²(x) and replace tan²(x) with sin²(x)/cos^2(x).

^{I wouldn't do this, but I would take a look at tanx and what the derivative is, it does become pretty hard though and you need a trig substitution afterwards, I think I did this exact problem before.}

 

[jfgobin]

A quick look at this table of derivatives should give some ideas.