Question

Integral of 6x^3 (x + 5) ^5 dx

Answer 1

Answer:

Integral of 6x^3 (x + 5) ^5 dx is

6x³ $(x+5)^6$/6 - [18x²  $(x+5)^7/42$ dx - {36x $(x+5)^8/336$ - 36$(x+5)^9/3024$}] + c ,     ( where c is an arbitrary constant)

Step-by-step explanation:

  $\int\ 6x^3 (x + 5) ^5 \, dx$

= 6x³ $\int\ (x + 5) ^5 \, dx$ - $\int${$\frac{d}{dx} (6x^3) \int\ (x + 5) ^5 \, dx$}dx

= 6x³ $(x+5)^6$/6 - $\int$ 18x² $(x+5)^6$/6 dx

= 6x³ $(x+5)^6$/6 - [18x²  $(x+5)^7/42$ dx - $\int$ {36x $(x+5)^7/42$}dx ]

= 6x³ $(x+5)^6$/6 - [18x²  $(x+5)^7/42$ dx - {36x $(x+5)^8/336$ - $\int$ 36 $(x+5)^8/336$ dx }]

= 6x³ $(x+5)^6$/6 - [18x²  $(x+5)^7/42$ dx - {36x $(x+5)^8/336$ - 36$(x+5)^9/3024$}] + c

                                                                         ( where c is an arbitrary constant)