Q.1 Find the Laplace transform for the following 1. t² sin 3t -21 2. t cos³t 3. te sint 5. te ³t sin 3t 6. te cos 2t 7. te ³1 sin² t 2t 9. t (2 sin 3t - 3 cos 3t) 10. te 2¹ (cost-sint) -21 12. te' sin 2t cost 13. te sinh 4t 15. t cos(at - a) 16. (t + sin 2t)² 19. e' sin 4t.cos 2t 18. cosat.sinhat 21. coshat.sin at 24. coshat.cos at 22. cos 3t.cosh 4t 25. t²-3t+5+e²¹² cosht sint -41 27. e4¹3/2 28. e е 30. e2¹ cos2 tcost 31. e²¹ (1+1)² e2t 4. te ³t sin 2t 8. t (2 sin 3t+e +e²¹) 11. e-2¹ (2 tcos2t+sin 2t) 4 14. te3 sinh 2t 17. (t sinh 2t )? 20. e-2¹ (2 cos 3t -3 sin 3t) 23. teat+sin³t 26. cosh at cosbt -31 29. e 32. cosh 4 tsin 3t cos 2t sint e²

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