# How do you find the definite integral of #t^3(1 + t^4)^3 dt# from #[-1, 1]#?

The quick way

The long way

So the integral becomes

The very long way

Finish integrating

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To find the definite integral of ( t^3(1 + t^4)^3 ) with respect to ( t ) from ( -1 ) to ( 1 ), you can use integration techniques. One common approach is to first expand ( (1 + t^4)^3 ) using the binomial theorem, then integrate each term separately, and finally evaluate the result at the upper and lower limits of integration. Alternatively, you can use a computer algebra system or integral tables to compute the integral directly.

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