Evaluate the following integrals using له 00 +2 e dx = √πT (a) o 19x-e 2X (6) 13√x e dx ㅠ

4. √√√x(2x¹1)¹/2 dx

Find an expression in a and b for the value of the definite integral:∫ba [2x2 + √x + 5]dx

Which of the following is equal to the integral in the picture? A. 2/3  B. -(1/3)  C. -(2/3)  D. 1/3  E. -(1/2)

Evaluate 3+√3 3 13 dx 10+ x² - 6x 3+√√√3 13 dx S 10+x²- - 6x 3 (Simplify your answer. Type an exact answer, using tas needed.) =

Find an expression in a and b for the value of the definite integral: ∫ ba[9x 2 + √x − 8] dx.

← 1. Find the indefinite integral of each of the following: a. fx sin2x dx x² sin 2xdx d. [xc g. ²2te-2tdt a. j. g. S 2. Find the indefinite integral of each of the following: Se5x dx b. [ sin4xdx 3x² d. ſ. dx x³ X +5 XCOS xdx e√x dx √x (e*+1)7e* dx a. d. S a. b. m. By using the substitution t= x−1, find n. By using the substitution x= 3sint, find X+3 (x+1)(x+2) x³ x+3x+2 3. Find the integral of each of the following: X-9 2x²-3x+1 dx dt ICON 2202 b. = kx = e. fx lnx dx 6xt² C e. dx ||| h. [x²√x³ +2dx k. [xcos(x² + 1) dx COS X dx 1+ sin x dx b. S e. 2x² +7x+7 X+2 a O X-2 (x-1)² 1 9-² dx dx c. S f. ²te²t dt C. [3cos 3xdx 1 f. S dx xln x dx % 3x² (x³ 3 +10) ³ I. [ e3cos2x sin 2xdx .dx. C. 4. Find the general solution of the following differential equation: dx dt f. xe Xdx S x² +3 x² + 3x 2 X X-1 2 4x². < + X dx -dx dx Page 1

Evaluate the indefinite integral 3x² S- dx x³√√x6-1 O to sec-1. 3 +C +3 sec-1. 1X/²³ +C 3 sec-1²+C 3 sec¹|x³| +C O

Please answer the questions with steps and correct answer

Evaluate the following integral by using an appropriate method. -10x-9x3- 48x2 - 13x 48 dx (x³ + 2x)(2x² + 3)