Trig Integrals - How is what I am doing wrong?

[MathHawk]

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.

 

[Mark44]

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.

 

[MathHawk]

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)?

 

[Random Variable]

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