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If inte^(ax)cosbx dx=(e2x)/(29)f(x)+C , ...

If `inte^(ax)cosbx dx=(e2x)/(29)f(x)+C` , then f'' (x)=

A

29 f (x)

B

`-29 f(x)`

C

25 f(x)

D

`-25 f(x)`

Text Solution

Verified by Experts

The correct Answer is:
d
We have , `inte^(ax)cosbx dx=(e^(ax))/(a^(2)+b^(2))(a cos bx +b sinbx)+C`
`rArr(e^(2x))/(2^(2)+5^(2))f(x)+C (e^(ax))/(a^(2)+b^(2))(a cos bx +b sin bx)+C`
`rArr a=2 , b =5 and f(x) =a cos bx +b sin dx`
`rArr f '' (x) =-b^(2)f(x)rArrf''(x)=-25f(x)`
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OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Solved Example
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