Question

integral of sin^50000x cosx​

Answer 1

Answer:

sin⁵⁰⁰⁰¹x/50001 + C

Step-by-step explanation:

Let, sinx = z

Taking differentials, we get

d (sinx) = dz

or, cosx dx = dz

Then ∫ sin⁵⁰⁰⁰⁰x cosx dx

= ∫ z⁵⁰⁰⁰⁰ dz

= z⁵⁰⁰⁰⁰⁺¹/(50000 + 1) + C

where C is constant of integration

= z⁵⁰⁰⁰¹/50001 + C

= sin⁵⁰⁰⁰¹x/50001 + C

This is the required integral.

Rules:

• ∫ sinx dx = - cosx + C

where C is constant of integration

• ∫ cosx dx = sinx + C

where C is constant of integration

• ∫ xⁿ dx = xⁿ⁺¹/(n + 1) + C, n is any rational number

where C is constant of integration