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Integrals

Evaluate the following integrals:
(1)The integral of (6sin[2x])/sin(x)dx=____+C
(2)The integral of (7-x)(3+[x^2])dx=____+C
(3)The integral from 3 to 7 of ([t^6]-[t^2])/(t^4)dt=____+C
(4)The integral of (6sin[x])/(1-sin^2[x])dx=____+C

Solution Preview

(1)
sin(2x)=2sin(x)cos(x) ---> 6sin(2x)/sin(x)= 12cos(x) and thereforte the integral is:

12sin(x)+C

(2)
Mulitply the terms:
(7-x)(3+x^2)= ...

Solution Summary

This shows how to evaluate integrals with fractions and sine functions.

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