Integrating by parts :

=x*integral(4^x)dx - integral(d/dx(x)*integral(4^x)dx)dx
=x(4^x)/ln4 - integral(1*4^x/ln4)dx
=x(4^x)/ln4 - (1/ln4)*integral(4^x)dx
=x(4^x)/ln4 -(1/ln4)*(4^x)/ln4 + C
=x(4^x)/ln4 - 4^x/ln^2(4) + C .
option (A) is correct.
QUESTION 8 | * 4* dx = O A. x(41) 4* In 4 +C In24 OB. (41) + In4 In24 to OC x2 (4*) 2(In 4) +C 4- OD. x(4+) In4 to In24 O E x 4" - 4* +C
QUESTION 5 | * 4* dx= 4* OA. x(44) In 4 +C In24 O B. x(4") In 4 + 4" In24 +C ос. x 4" - 4* +C OD. x² (4²) 2(In 4) +C DE x² (41) 45 + + In 4 In-4
QUESTION 4 x 4 dx= OA. x²(4") 2(In 4) +C O B. x(4") In 4 + 4.1 In24 +C oc x(4") 4* + +C In 4 In²4 OD x 4" - 4" +C O E *(4) In 4 4" In24 +C
Graph the function fix) 2- for x 2 1 - 3x, for x 2 OA OB Ос. OD Click to select your answer 30 004
Question 23 Which would be formed when 2-methylpropanal is dissolved in D 20 containing Dt? OA D CH.CHCHOD CH3 OB. CH.COM CH CDCH CH Ос. 0 CHCHCH CHED OD O CH.CHCD CH Е. O CH₃COCO 29 MacBook Air 3 $ 4. 5
Solve. 2x2 - 10x= -9 OA -5177 4 5377 OB. 2 5117 4 - 5+ OD 2
Use the substitution formula to evaluate the integral. 1/2 COS X s dx (5+5 sin x) 0 3 OA 1000 OB 3 200 OC. 3 200 OD. 12 125
Evaluate the integral using the given substitution. OA. $x*(88 - 4) *dx, u=x2-4 35x25 - 4+0 O B. 15 (85 - 4) + 12 / 3 (x3 - 4) + OD. 13 (x² - 4) + c +C Oc. +C
Use a change of variables to evaluate the following indefinite integral. ( (Vx+5) 4 3 dx J2V Determine a change of variables from x to u. Choose the correct answer below. OA. u= (x + 5)^ OB. u= VX +5 OC. Uz OD. u= Write the integral in terms of u. (Vx+5) dx = du 28x Evaluate the integral (Vx+5)* dx=0 2/8 Click to select your answer(s).
Evaluate the integral. 45 SS (2x2y=6xy) dy dx jjcz 00 OA. 10 3 OB. 200 3 OC. 50 3 wia wie OD. 40 3