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Evaluate following integrals.
(a) ∫ 3ex + 5 cos x -10 sec2 x dx
(b) ( 23/ (y 2 + 1) + 6 csc y cot y + 9/ y dy
Solution
∫ 3ex + 5 cos x -10 sec2 x dx = 3ex + 5 sin x -10 tan x + c
(b) (( 23/ (y 2 + 1) + 6 csc y cot y + 9/ y dy
In this one we'll just utilizes the formulas from above. There are just multiplicative constants and thus can be avoid while we integrate each of the term and then once we're done integrating a given term simply we put the coefficients back in.
∫ 23/(y2+1) + 6 csc y cot y +(9/y) dy = 23 tan -1 y - 6 csc y + 9 ln |y| + c
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