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Evaluate int(3x^(2)"tan"(1)/(x)-x"sec"^(...

Evaluate `int(3x^(2)"tan"(1)/(x)-x"sec"^(2)(1)/(x))dx`.

A

`x^(3)" tan"(1)/(x)+C`

B

`x^(2)" tan"(1)/(x)+C`

C

`x " tan"(1)/(x)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I=int(3x^(2)"tan"(1)/(x)-x" sec"^(2)(1)/(x))dx`
`rArrI=intunderset(II)(3x^(2))underset(I)("tan")(1)/(x)+dx-int"sec"^(2)(1)/(x)dx`
`rArrI=x^(3)" tan"(1)/(x)x " sec"^(2)(1)/(x)dx-intx " sec"^(2)(1)/(x)dx+C`
`=x^(3) "tan" (1)/(x)+C`
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