a) 0.048
b) 0.144
c) 5.827
d) 23.308
e) 1,640.250
how will i work it out
2 Answers

∫(lnx)³/x dx = ∫(lnx)³(1/x) dx
u = lnx
du = 1/x dx
= ∫u³ du = (u^4)/4 + C = ¼[(lnx)^4] + C
F(1) = 0
¼[(ln(1))^4] + C = 0
¼(0)^4 + C = 0
C = 0
F(x) = ¼[(lnx)^4]
F(9) = ¼[(ln(9))^4] = 5.827 ; therefore the answer is (c)
Source(s): Integral Calculator: http://integrals.wolfram.com/index.jsp
StepbyStep Derivative Calculator: http://calc101.com/webMathematica/derivatives.jsp
Another Integral and Derivative Solver: http://www.mathanswerkey.com/solution.php?math=cal 
â«(lnx)^3 / x dx
= â«(lnx)^3 d(lnx)
= (1/4) (lnx)^4 + c
F(1) = 0
=> c = 0
=> F(x) = (1/4)(lnx)^4
=> F(9) = (1/4)(ln9)^4
= 5.827.