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# Trigonometric Integrals and Integration by Substitution

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Evaluate the integral

1) âˆ« (sin^3 (x)) (cos^2 (x)) dx
2) âˆ« ( sin^4 (x)) (cos^5 (x)) dx
3) âˆ« ( sin^6 (x)) (cos^3 (x)) dx
4) âˆ« ( sin^3 (mx)) dx
5) âˆ« (from 0 to pi/2 on top) (cos^2 (theta)) dtheta
6) âˆ« (from 0 to pi/2 on top) (sin^2 (2theta)) dtheta
7) âˆ« (from 0 to pi on top) (sin^4 (3t)) dt
8) âˆ« (from 0 to pi on top) (cos^6 (theta)) dtheta
9) âˆ« ( 1 + cos theta)^2 dtheta
10) âˆ« (x) (cos^2 (x)) dx
11) âˆ« ( sin^3 (x)) (SQRT(cos (x)) dx
12) âˆ« (cos (theta) (cos^5(sin(theta))) dtheta
13) âˆ« (cos^2 (x)) (tan^3 (x)) dx
14) âˆ« ( cot^5 (theta)) (sin^4 (theta)) dtheta
15) âˆ« [( 1 - sinx) / (cosx) ]dx
16) âˆ« ( sin 2x) (cos^2 (x)) dx
17) âˆ« ( sec^2 (x)) (tan (x)) dx
18) âˆ« ( tan^2(x) dx
19) âˆ« ( sec^6(t)) dt
20) âˆ« (from 0 to pi/4 on top) (sin^4 (theta)) (tans^4 (theta)) dtheta
21) âˆ« (from 0 to pi/3 on top) (tan^5 (x)) (sec^4 (x)) dx
22) âˆ« ( tan^3 (2x)) (sec^5 (2x)) dx
23) âˆ« ( tan^3 (x)) (sec (x)) dx
24) âˆ« (from 0 to pi/3 on top) (tan^5 (x)) (sec^6 (x)) dx
25) âˆ« ( tan^5 (x)) dx
26) âˆ« ( tan^3 (theta)) / (cos^4 (theta)) dtheta
27) âˆ« ( tan^2 (x)) (sec (x)) dx
28) âˆ« ( cot^3 (alpha)) (csc^3 (alpha)) dalpha
29) âˆ« ( csc^4 (x)) (cot^6 (x)) dx
30) âˆ« ( csc (x)) dx
31) âˆ« ( sin (5x)) (sin (2x)) dx
32) âˆ« [( dx) / ((cos (x)) - 1)] dx
33) âˆ« [( 1 - tan^2 (x)) / (sec^2 (x))] dx
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