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Integral of sec^4(x)*tan(x) dx? Please check my answer? see the attachment

For my answer, I let u =tanx

so du=sec^2x dx

BUT WHEN I DO THIS MAPLE SOFTWARE, I GOT A DIFFERENT ANSWER WHICH IS Sec^4(x)/4

WHY IS THIS HAPPENING?

I AM SURE I AM RIGHT!

When these two formulas are put in Excel, they are seen to differ by 1/4 no matter what value of x is used. This means they are really the same with a different value of C in the integral.

We can rewrite tan^2 / 2 + tan^4 / 4 as (tan^2/4)(2+tan^2).

Multiply it out - it checks out.

Now since 1 + tan^2 = sec^2 and tan^2 = sec^2 - 1, this can be rewritten.

[(sec^2 - 1)/4](1 + sec^2) = (sec^2 - 1)(sec^2 + 1)/4.

Multiplying this out gives (sec^4 - 1)/4.

From there, we can see the only difference is 1/4, which is what Excel gave me.

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