Evaluate the indefinite integral of y=x^2(x^3+1)^4.

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We have to find the integral of y=x^2(x^3+1)^4.

Let t = x^3+1

dt/dx = 3x^2

=> x^2 dx = (1/3) dt

Now Int [ x^2(x^3+1)^4 dx]

=> Int [ (1/3)* t^4 dt]

=> (1/3) t^5 / 5

=> t^5 / 15

replace t with x^3 + 1

=> (1/15)*(x^3 + 1)^5 + C

Therefore the required integral is (1/15)*(x^3 + 1)^5 + C.

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