Integate the following- Sec2x/(secx+tanx)9/2

Asked by Satendra Pal | 2nd Nov, 2012, 05:39: PM

Expert Answer:

Let secx + tanx = t .............. [1]

thus, { secx - tanx } = 1 / t .....[2]

solving , 1 & , 2 , we get,

secx = t2 + 1 / 2t .....[3]

Now , again consider secx + tanx = t

Differentiating both sides , with respect to 'x ' , we get,

secx* tanx + sec2 x = dt / dx

secx { secx + tanx } = dt / dx

secx { t } = dt/ dx ... ..[4]

putting the value of secx from [3] in [4], we get,

dx = dt * 2 / [ t2 + 1 ]

Now, put the value of t to get the answer.

Answered by  | 2nd Nov, 2012, 05:51: PM

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