### Author Topic: integral problems  (Read 639 times)

#### chloe

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##### integral problems
« on: November 11, 2018, 12:41:18 AM »

\int \frac{-\sin{3t}\times9\sec^2{3t}}{3} \,dt\\

« Last Edit: November 11, 2018, 01:39:23 PM by chloe »

#### Chuanxin Zhang

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##### Re: integral problems
« Reply #1 on: November 11, 2018, 12:56:16 AM »

\int \frac{-\sin{3t}\times9\sec^2{3t}}{3} \,dt\\

= \int \frac{-3sin{3t}}{cos^2{3t}} \,dt\\
=\int \frac{1}{cos^2{3t}} \,d(cos{3t})\\

let  m=cos3t

\int \frac{1}{cos^2{3t}} \,d(cos{3t})\\
=\int \frac{1}{cos^2{3t}} \,dm\\
=\int \frac{1}{m^2}\,dm\\
=\frac{-1}{m}\\
=\frac{-1}{cos3t}\\

« Last Edit: November 11, 2018, 01:41:50 PM by Chuanxin Zhang »

#### Victor Ivrii

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##### Re: integral problems
« Reply #2 on: November 11, 2018, 01:13:57 AM »
$*$ IS N OT A SIGN OF MULTIPLICATION

#### Chuanxin Zhang

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##### Re: integral problems
« Reply #3 on: November 11, 2018, 01:43:07 PM »
Fixed! I thought * was the multiplication sign by default:(