Question

Integrate :-

Answer 1

@Fifciol

Answer 2

cos2x=2cos^2x-1

Answer 3

first you need to know trig properties.
cos^2 = 1/2*cos(2x) + 1/2

now integral (1/2*cos(2x)+1/2), you can factor out a 1/2

integral(1/2) + 1/2 * integral(cos(2x))

u = 2x, du = 2dx

1/4 * integral(cos(u)du) + integral(1/2*dx)

integral of cos(u) = sin(u)
integral of 1/2dx = x/2
sin(u)/4 + x/2 + c1

u = 2x

sin(2x)/4 + x/2 + c1

now using properties to change sin(2x)

1/2*(x+sinxcosx)

Answer 4

\[\cos2x=\cos^2x-\sin^2x=\cos^2x-(1-\cos^x)=2\cos^2x-1 \rightarrow \cos^2x=\frac{1+\cos2x }{ 2 }\]

Answer 5

basically answer is same as last one.instead of - there u get +

Answer 6

Thank You Sir....