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INTEGRATION BY SUBSTITUTION Solve by using substitution method 1. 3x + x2 (e3x + x3)3 dx 2. ezx (e2x + 1)3 dx 3. In 5x 4. 3 - dx - dx X x In x 5. 6. x (x 2 + 1) 3/2 dx e2-x dx 7. x 2 8. dx ezx+3 dx 2 x3 - 3 9. x(x - 1)5 dx 10. x2 (1 - x) 6 dx Answers : 1. 1 2. (e2x + 1 ) 4 2 + c 3. (In 5x) 2 6(e3x + x3)2 + C + C 8 2 4. 3 In In x + C 5. 0.93 6. e-1 7 0.523 8 64.164 9. (x - 1)' (x - 1)6 10. -+c (1- x)' (1-x)8 (1-x)9 7 9 -+cBASIC INDEFINITE AND DEFINITE INTEGRAL Find the indefinite integral and evaluate the definite integral 1 . u3 + 2u2 - u dx 2 . du 3u 3. x* - 1 4 . dx (2x + 1) (x - 2) dx 72 5 . 6. 72 ( x4 - 2x2 + 1) dx ex dx 7. ( x2 - 2x + 2) dx 8. ( x3 + x ) dx 2. [ ( 1+ 2 + ex ) dx 10. (2x3 - 3) dx Answers : 1. 2 2. 3. x3/2 + 4Vx + C " + C 1 -+- WII 9 + 3 3 3 X 4. 3 5. 6. e - 1 WIN x3 x2 - 2x + C 3 - 2x - =+C 7. 6 8. 9. 1 + In 2 +e2 - e 10. 34