# Trig Integrals - How is what I am doing wrong?

I like to work these problems out and then check them with online integral calculators.

## Homework Statement

$$\int$$$$^{\pi/4}_{0}$$tan2x * sec4x dx

## Homework Equations

$$\frac{d}{dx}$$tanx = sec2x
sec2x = 1 + tan2x

## The Attempt at a Solution

This seems so simple, using the identities and u substitution:

$$\int$$$$^{\pi/4}_{0}$$tan2x * sec4x dx
$$\int$$$$^{\pi/4}_{0}$$tan2x * sec2x * sec2x dx
$$\int$$$$^{\pi/4}_{0}$$tan2x * (tan2x + 1) * sec2x dx
$$\int$$$$^{\pi/4}_{0}$$(tan4x + tan2x) * sec2x dx

Now: u = tanx, du = sec2x dx. tan $$\pi/4$$ = 1, tan 0 = 0/

$$\int$$$$^{1}_{0}$$(u4 + u2) du

= [$$\frac{1}{5}$$u5 + $$\frac{1}{3}$$u3]$$^{1}_{0}$$

$$\frac{1}{5}$$ + $$\frac{1}{3}$$ - (0 + 0) = $$\frac{8}{15}$$

Therefore:

$$\int$$$$^{\pi/4}_{0}$$tan2x * sec4x dx = $$\frac{8}{15}$$

Online indefinite integral calculators disagree with my indefinite integral, and the definite integral calculator I tried timed out. This looks flawless to me, but apparently I'm an idiot.

Thank you very much in advance for any help.

Last edited:

## Answers and Replies

Mark44
Mentor
I like to work these problems out and then check them with online integral calculators.

## Homework Statement

$$\int$$$$^{\pi/4}_{0}$$tan2x * sec4x dx

## Homework Equations

$$\frac{d}{dx}$$tanx = sec2x
sec2x = 1 + tan2x

## The Attempt at a Solution

This seems so simple, using the identities and u substitution:

$$\int$$$$^{\pi/4}_{0}$$tan2x * sec4x dx
$$\int$$$$^{\pi/4}_{0}$$tan2x * sec2x * sec2x dx
$$\int$$$$^{\pi/4}_{0}$$tan2x * (tan2x + 1) * sec2x dx
The expression below does not follow from the one above.
$$\int$$$$^{\pi/4}_{0}$$tan4x * tan2x * sec2x dx

Now: u = tanx, du = sec2x dx. tan $$\pi/4$$ = 1, tan 0 = 0/

$$\int$$$$^{1}_{0}$$(u4 + u2) du

= [$$\frac{1}{5}$$u5 + $$\frac{1}{3}$$u3]$$^{1}_{0}$$

$$\frac{1}{5}$$ + $$\frac{1}{3}$$ - (0 + 0) = $$\frac{8}{15}$$

Therefore:

$$\int$$$$^{\pi/4}_{0}$$tan2x * sec4x dx = $$\frac{8}{15}$$

Online indefinite integral calculators disagree with my indefinite integral, and the definite integral calculator I tried timed out. This looks flawless to me, but apparently I'm an idiot.

Thank you very much in advance for any help.

You're right. However, I don't have that on paper (I have the + in place of the *). It's corrected on here when I use u substitution, and it doesn't affect my answer. Is there anything else, or did I just whoop a computer integral calculator (doubtful)?

You apparently don't know how to use a computer integral calculator because your answer (and procedure) is correct.