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Integrate dx/2x 3?

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Integrate dx/2x 3?

To integrate the function dx/2x3, we can use the formula for the indefinite integral of a rational function:

∫dx/p(x) = ln |p(x)| + C

where p(x) is a polynomial and C is the constant of integration.

In this case, p(x) = 2x3, so we can write:

∫dx/2x3 = ln |2x3| + C

Evaluating this integral gives us:

∫dx/2x3 = ln |2x3| + C = ln |2| + ln |x3| + C = ln |2| + 3 * ln |x| + C

This is the indefinite integral of dx/2x3. The constant of integration C can take on any value, so the indefinite integral of dx/2x3 is equal to ln |2| + 3 * ln |x| + C for any value of C.

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