The indefinite integral of (1/x^2)*dx is -1/x+C.
The integral of 1 + x2 is x + 1/3 x3 + C.
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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
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The indefinite integral of (1/x^2)*dx is -1/x+C.
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I will assume that this is sopposed to be integrated with respect to x. To make this problem easier, imagine that the integrand is x raised to the negative 3. The integral is 1/(-2x-2) plus some constant c.
(1+x)/(x^2+1) Let x^2+1 =u 2x dx = du x dx = du/2 (1+x) / (x^2+1) = 1/(x^2+1) + x / (x^2+1) Integral of x dx / (x^2+1) = (1/2) integral du / u = 1/2 ln|u| --(1) Integral of 1 / (x^2+1) = arctan(x) --(2) Adding (1) and (2) Integral (1+x)/(x^2+1) = (1/2) ln(x^2+1) + arctan(x) + C
-(x-1)-1 or -1/(x-1)
The integral of 1 + x2 is x + 1/3 x3 + C.
arctan(x)
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