Integrate the following with respect to x : coseccosec xlog(tan x2)

Integrate the following with respect to x :

`("cosec" x)/(log(tan x/2))`

योग

`int ("cosec" x)/(log(tan x/2)) "d"x`

Put `log (tan x/2)` = u

`1/(tan x/2) xx sec^2 x/2 xx 1/2 xx "d"x` = du

`cot x/2 xx 1/(cos^2 x/2) xx 1/2 xx "d"x` = du

`(cos x/2)/(sin x/2) xx 1/(cos^2 x/2) xx 1/2 xx "d"x` = du

`1/(2sin x/2 cos x/2) "d"x` = du

`1/sinx "d"x` = du

`"cosec" x "d"x` = du

∴ `int ("cosec" x)/(log(tan x/2)) "d"x = int "du"/"u"`

= `log |"u"| + "c"`

`int ("cosec" x)/(log(tan x/2)) "d"x = log |log(tan x/2)| + "c"`

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अध्याय 11: Integral Calculus - Exercise 11.6 [पृष्ठ २०६]

अध्याय 11 Integral Calculus
Exercise 11.6 | Q 7 | पृष्ठ २०६

Find the volume of solid generated by rotating the area bounded by x²+y² =36 and the lines x = 0, x = 3 about X -axis.

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`(x + 1)/((x + 2)(x + 3))`

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`x^2/(1 + x^6)`

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sin⁵x cos³x

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x³ sin x

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`"e"^x sec x(1 + tan x)`

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`1/((x + 1)^2 - 25)`

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`sqrt(x^2 - 2x - 3)`

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`sqrt(9 - (2x + 5)^2`

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`sqrt(81 + (2x + 1)^2`