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Evaluate `int_0^1 32(x^2+1)^7 xdx` definite integral

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Evaluate `int_0^1 32(x^2+1)^7 xdx`

definite integral

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Evaluate`int_0^1 32(x^2+1)^7xdx` :

Let `u=x^2+1,du=2xdx` . When x=0,u=1; when x=1 u=2.

We can write the integral as `int_0^1 16(x^2+1)^7 2xdx` or:

`int_1^2 16u^7du=16int_1^2u^7du=16[u^8/8 |_1^2]=16[32-1/8]=510`

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`int_0^1 32(x^2+1)^7xdx=510`

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