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## Homework Statement

∫e^(-x)(1-tanx)secx dx

**2. Attempt at a solution**

I know ∫e^x(f(x)+f'(x))=e^x f(x)

and I intuitively know f(x) could be secx here and therefore f'(x) will be secxtanx but I can't figure out how to reach that

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- Thread starter Krushnaraj Pandya
- Start date

- #1

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∫e^(-x)(1-tanx)secx dx

I know ∫e^x(f(x)+f'(x))=e^x f(x)

and I intuitively know f(x) could be secx here and therefore f'(x) will be secxtanx but I can't figure out how to reach that

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It is almost handed over on a silver platter: if ##\ \ -\displaystyle {\sin x\over \cos^2 x}\ ## is ##f'(x)##, what do you have left over for ##f(x)## ?

- #3

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I know the derivative of -secx is -sinx/cos^2 x. the first trouble is that the problem has e^(-x) instead of e^(x). the second is that -sin/cos^2 is the derivative of -secx, not secx. I'm sure these two things tie together somehow through a basic simplification but I can't figure this basic simplification out

It is almost handed over on a silver platter: if ##\ \ -\displaystyle {\sin x\over \cos^2 x}\ ## is ##f'(x)##, what do you have left over for ##f(x)## ?

- #4

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AHHH! how INCREDIBLY stupid of me. I just had to put -x=t (sorry you had to read this question). I'm never going to be a scientist this way...

It is almost handed over on a silver platter: if ##\ \ -\displaystyle {\sin x\over \cos^2 x}\ ## is ##f'(x)##, what do you have left over for ##f(x)## ?

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