The integral of 1 + x2 is x + 1/3 x3 + C.
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x2(x3 + 1) is the best you can do there.
x2 + 7x + 6 = (x + 6) (x + 1)
For it to be a definite integral, you would need to specify a range. We can however give you the indefinite integral. The easiest way to do this is to think of it not as a fraction, but as a negative exponent: 1/x2 = x-2 It then becomes quite easy to integrate, as we can say in general: ∫(axn) dx = ax(n + 1) / (n + 1) + C In this case then, we have: ∫(x-2) dx = -x-1 + C, or -1/x + C
3x2 + 2x + 3 + x2 + x + 1 = 4x 2+ 3x + 4
square root of (x2 + 1) = no simplification (square root of x2) + 1 = x + 1