Question

solve this question​

Answer 1

Heya!

put 3 - 2x = z

Differentiate both sides w.r.t x we have

-2dx = dz

Integration of -2Sin^7 ( z ) dz

integration of -2 { Sin^6 (z) × Sin ( z ) }dz

integration of -2{ ( 1 - Cos² z )³ Sin z }dz

put Cos z = t

Differentiate both sides w.r.t z we have

- Sin z = dt/dz

dz =- dt/Sin z

integration of 2 { (1 - t²)³ dt

integration of 2 { 1 - t^6 - 3t² + 3t⁴ } dt

2 { t - (t^7)/7 - t³ + (3/5)t^5

2 { Cos z - (Cos^7z )/7 + (3/5) Cos^5z }

2 { Cos ( 3 - 2x ) - Cos^7 ( 3 - 2x ) /7 + (3/5) Cos^5 ( 3 - 2x ) } + C

Where c is called constant of integration.

Answer 2

Answer:

Step-by-step explanation:

Indefinite integration:-At first,we apply method of substitution.

We substitute 3-2x=t

We get a new integral of

(-sin^7(t))/2,with respect to t.

We break sin^7(t) as sin^6(t).sint.

We convert it in form of cos,sin,

and then substitute cost=u

Then we get a simple integral, calculated by simple formula.

Formulae used:-

(a-b)^3=a^3-b^3-3ab(a-b)

Integral of x^n is (x^(n+1))/(n+1)