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Question
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Solution
`int (3 sec^2 x - 4/x + 1/(xsqrt(x)) - 7)dx`
= `3int sec^2x dx - 4 int 1/x dx + intx ^(-(3)/(2)) dx - 7 int 1 dx`
= `3 tan x - 4 log |x| + (x ^(- 3/2 + 1))/(-3/2 + 1) - 7x + c`
= `3 tan x - 4 log |x| + (x ^(- 1/2 ))/(-1/2) - 7x + c`
= `3 tan x - 4 log |x| + (-2x^(-1/2)) - 7x + c`
= `3tan x - 4 log |x| - 2/sqrt(x) - 7x + c`
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