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Solution - Integrate : sec^3x w. r. t. x. - Methods of Integration - Integration by Parts

Question

Integrate : sec3 x w. r. t. x.

Solution

`I = intsec^3x dx`

`I =int secx.sec^2x dx`

`I =secx.intsec^2xdx-int[d/dx(secx).int sec^2x dx] dx`

`I =secx.tanx-int secx.tanx.tanx dx`

`I =secx.tanx-int secx(sec^2x -1)dx`

`I =secx.tanx-int [sec^3x-secx]dx`

`I =secx.tanx-int sec^3x + int secxdx`

`I =secx.tanx - I + log|secx + tanx| + c`

`2I =secx.tanx + log|secx + tanx| + c`

`therefore I =1/2(secx.tanx + log|secx + tanx|) + c`

Is there an error in this question or solution?

APPEARS IN

2014-2015 (March)
Question 5.1.1 | 3 marks
Solution for question: Integrate : sec^3x w. r. t. x. concept: Methods of Integration - Integration by Parts. For the courses HSC Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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