Basic Trigonometric Integration Questions

1. Integrate: ( int sin(x) , dx )
2. Integrate: ( int cos(x) , dx )
3. Integrate: ( int tan(x) , dx )
4. Integrate: ( int cot(x) , dx )
5. Integrate: ( int sec(x) , dx )
6. Integrate: ( int csc(x) , dx )
7. Integrate: ( int sin^2(x) , dx )
8. Integrate: ( int cos^2(x) , dx )
9. Integrate: ( int sec^2(x) , dx )
10. Integrate: ( int csc^2(x) , dx )
11. Integrate: ( int sin^3(x) , dx )
12. Integrate: ( int cos^3(x) , dx )
13. Integrate: ( int sec^3(x) tan(x) , dx )
14. Integrate: ( int csc^3(x) cot(x) , dx )
15. Integrate: ( int sin(x) cos(x) , dx )

Basic Trigonometric Integration Questions and Solutions

1. Integrate: ( int sin(x) , dx )
   Solution: ( -cos(x) + C )
2. Integrate: ( int cos(x) , dx )
   Solution: ( sin(x) + C )
3. Integrate: ( int tan(x) , dx )
   Solution: ( -ln|cos(x)| + C ) or ( ln|sec(x)| + C )
4. Integrate: ( int cot(x) , dx )
   Solution: ( ln|sin(x)| + C )
5. Integrate: ( int sec(x) , dx )
   Solution: ( ln|sec(x) + tan(x)| + C )
6. Integrate: ( int csc(x) , dx )
   Solution: ( -ln|csc(x) + cot(x)| + C )
7. Integrate: ( int sin^2(x) , dx )
   Solution: ( frac{1}{2} x – frac{1}{4} sin(2x) + C )
8. Integrate: ( int cos^2(x) , dx )
   Solution: ( frac{1}{2} x + frac{1}{4} sin(2x) + C )
9. Integrate: ( int sec^2(x) , dx )
   Solution: ( tan(x) + C )
10. Integrate: ( int csc^2(x) , dx )
    Solution: ( -cot(x) + C )
11. Integrate: ( int sin^3(x) , dx )
    Solution: ( -frac{1}{3} cos^3(x) + C )
12. Integrate: ( int cos^3(x) , dx )
    Solution: ( frac{1}{3} sin^3(x) + C )
13. Integrate: ( int sec^3(x) tan(x) , dx )
    Solution: ( frac{1}{2} sec^2(x) + C )
14. Integrate: ( int csc^3(x) cot(x) , dx )
    Solution: ( -frac{1}{2} csc^2(x) + C )
15. Integrate: ( int sin(x) cos(x) , dx )
    Solution: ( frac{1}{2} sin^2(x) + C ) or using substitution: ( frac{1}{2} cos^2(x) + C )