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Find the integral I=int x^2e^(x^3)cos(...

Find the integral
`I=int x^2e^(x^3)cos(x^3)dx`

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Consider the integrals I_(1)=int_(0)^(1)e^(-x)cos^(2)xdx,I_(2)=int_(0)^(1) e^(-x^(2))cos^(2)x dx,I_(3)=int_(0)^(1) e^(-x^(2))dx and I_(4)=int_(0)^(1) e^(-x^(1//2)x^(2))dx . The greatest of these integrals, is