Use limits of definite integrals to calculate each of the improper integrals in Exercises - dx - dx (x2 + 1) 41. Lo x2 + 1)² 42. /2 T/2 43. secx dx 44. tan xdx 0. In x dx Inx dx 45. 46. 1 1 dx xlnx 1 dx x Inx 47. 48. 1 dx x(ln x)? 1 dx x(In x)2 49. 50. 1 sin (1/x) dx x2 1 52. dx x(х — 1) 51. 1/т 2 1 1 53. dx dx x(x – 1) 54. 1 x(x– – 1) 00 55. lo x(x – 1) X – 2 dx 1) dx 56. x(x

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A: Since, you have asked multiple question, we will solved the first question for you. If you want any…

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A: #1 First perform long division to be able to perform partial fraction decomposition.…