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Why Is My Answer Wrong (trig integral)

agh, trig integrals are driving me nuts.

1. Homework Statement

the integral of

tanx sec^4x dx


2. Homework Equations



3. The Attempt at a Solution

tanx sec^4x dx
= sec^3 tanx secx dx

u = secx
du = tanx secx dx

so,
= u^3 du
= (u/4)^4
= (1/4)sec^4x
 

D H

Staff Emeritus
Science Advisor
Insights Author
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681
The final result looks good to me. You did make a mistake in an intermediate step, however; you should have had u^4/4, rather than (u/4)^4.

What makes you think your answer is wrong?
 
Yes, your final answer should be sec^4x/4, but you forgot one thing: +C. This is important.
 
O, ok. The book substitutes u = tanx to get (1/4)tan^4x + (1/2)tan^2x + C, and that got me confused.

Thanks
 
Just the same, since sec^2x=1+tan^2x
 

HallsofIvy

Science Advisor
Homework Helper
41,683
865
The way I would have done this would have been to convert immediately to sine and cosine (I get so confused with those other trig functions!): tan(x) sec^4(x)= sin(x)/cos^5(x)[/itex] and then the substitution u= cos(x), du = -sin(x) dx gives the integral
[tex]-\int du/u^5= -\int u^{-5}du= (1/4)u^{-4}+ C= (1/4)cos^{-4}(x)+ C= (1/4)sec^4(x)+ C[/itex]
again, "just the same".
 

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