Evaluate the integral below.

Question

Evaluate the integral below.

 

∫ 3??^−4?? ????

Answer 1

I'm not sure about all the question marks; if the integral is meant to be ∫3x^-4dx,

you would simply build the solution around x^-3 because x^-3 differentiates back to

-3x^{(-3 − 1)} or -3x^(-4) or -3x^-4.

This almost gives the integrand 3x^-4 above. Put a negative sign to the left of x^-3

and add a "C" (for some undetermined constant or exact number) to -x^-3 to obtain 

-x^-3 + C.

Test this answer by taking the derivative of -x^-3 + C: d(-x^-3 + C)/dx gives

[-(-3)x^{(-3 − 1)}] + 0 which will reduce to 3x^(-4) or 3x^-4, the original integrand above.