evaluate following integrals a int 3ex 5 cos

Question

Evaluate following integrals.

 (a) ∫ 3e^x + 5 cos x -10 sec²  x dx

 (b) ( 23/ (y ² + 1) + 6 csc y cot y + 9/ y dy

Solution

(a)    ∫ 3e^x + 5 cos x -10 sec² x dx

∫ 3e^x + 5 cos x -10 sec² x dx = 3e^x + 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

In the next problem we will take a look at a product & this time we're not going to be capable to just multiply the product out.  Though, if we recall the comment regarding simplifying a little this problem becomes simple.