1)integral of : a) cosx b) sinx c) e^x d) 1/y e) tanx f) tanx g) cotx h) (sec^2)x i) (cos^2)x

Answer 1

Here are the integrals of the functions you provided:

a) \(\int \cos x , dx = \sin x + C\)

b) \(\int \sin x , dx = -\cos x + C\)

c) \(\int e^x , dx = e^x + C\)

d) \(\int \frac{1}{y} , dy = \ln |y| + C\)

e) \(\int \tan x , dx = -\ln |\cos x| + C\)

f) \(\int \tan x , dx = -\ln |\cos x| + C\) (This is the same as e)

g) \(\int \cot x , dx = \ln |\sin x| + C\)

h) \(\int \sec^2 x , dx = \tan x + C\)

i) \(\int \cos^2 x , dx = \frac{1}{2}x + \frac{1}{4} \sin(2x) + C\)

Each integral includes the constant of integration \(C\) because these are indefinite integrals.