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Mathematics 17 Online
OpenStudy (anonymous):

What is the antiderivative of cos^3(x)+4/cos^2(x)?

OpenStudy (anonymous):

@amistre64

OpenStudy (amistre64):

can you clean up the notation, its a bit vague at the moment what the function is spose to be

OpenStudy (amistre64):

\[\frac{a^3+b}{a^2}\]or \[a^3+\frac{b}{a^2}\]

OpenStudy (anonymous):

it is \[\int\limits \frac{ \cos ^{3}x+4\ }{\cos ^{2} x }\]

OpenStudy (amistre64):

split the fraction

OpenStudy (anonymous):

wow im having really bad connection sorry about this

OpenStudy (amistre64):

its the site itself, its been broken for a while now

OpenStudy (anonymous):

so \[\cos x + \cos ^{-2}x\] ?

OpenStudy (amistre64):

pretty much cos^(-2) = sec^2 right?

OpenStudy (anonymous):

oh, wow that's really easy then

OpenStudy (amistre64):

\[\int\limits \cos x+4\ \sec ^{2} x \] yes, it is rather simple :)

OpenStudy (anonymous):

so then integral of that is -sinx + tanx

OpenStudy (anonymous):

-sinx+4tanx

OpenStudy (amistre64):

yep, dont forget the constant

OpenStudy (anonymous):

+C

OpenStudy (amistre64):

thatll do it

OpenStudy (anonymous):

thank you!

OpenStudy (amistre64):

yw

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