What is the indefinite integral of the function f(x)=x^4(x^5+5)^5?

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We have to find the indefinite integral of f(x)=x^4(x^5+5)^5.

Int [f(x) dx] = Int [ x^4(x^5+5)^5 dx]

let t = x^5 + 5

=> dt/dx = 5x^4

=> x^4 dx = dt /5

Int [ x^4(x^5+5)^5 dx]

=> Int [ (1/5) t^5 dt]

=> (1/5) t^6 / 6 + C

=> (1/30)*t^6 + C

replace t with x^5 + 5

=> (1/30)*( x^5 + 5)^6 + C

Therefore the required integral is (1/30)*( x^5 + 5)^6 + C

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