integration plz!!!!!!?

Question

hey guys, ive got a math question. its integration, it goes like this
∫ f(x) dx, from 4 to 8,
f(x) = ln(9-x) / [ln(9-x)+ln(3+x)]
plz answer as soon as possible!!! lol

Answer 1

Remember Ln(a) + Ln(b) = Ln (ab)

Answer 2

I could not find a closed form.
Integrating numerically,
. x . . . . . f(x) . . . . . . . . ∆A . . . . . . ∑∆A
4.00 , 0.4526808
4.05 , 0.4502254 , 0.0225727 , 0.0225727
4.10 , 0.4477564 , 0.0224495 , 0.0450222
4.15 , 0.4452730 , 0.0223257 , 0.0673479
4.20 , 0.4427745 , 0.0222012 , 0.0895491
4.25 , 0.4402600 , 0.0220759 , 0.1116250
4.30 , 0.4377288 , 0.0219497 , 0.1335747
4.35 , 0.4351799 , 0.0218227 , 0.1553974
4.40 , 0.4326125 , 0.0216948 , 0.1770922
4.45 , 0.4300257 , 0.0215660 , 0.1986582
4.50 , 0.4274185 , 0.0214361 , 0.2200943
4.55 , 0.4247901 , 0.0213052 , 0.2413995
4.60 , 0.4221393 , 0.0211732 , 0.2625727
4.65 , 0.4194652 , 0.0210401 , 0.2836129
4.70 , 0.4167668 , 0.0209058 , 0.3045187
4.75 , 0.4140428 , 0.0207702 , 0.3252889
4.80 , 0.4112923 , 0.0206334 , 0.3459223
4.85 , 0.4085140 , 0.0204952 , 0.3664174
4.90 , 0.4057067 , 0.0203555 , 0.3867730
4.95 , 0.4028691 , 0.0202144 , 0.4069873
5.00 , 0.4000000 , 0.0200717 , 0.4270591
5.05 , 0.3970979 , 0.0199274 , 0.4469865
5.10 , 0.3941614 , 0.0197815 , 0.4667680
5.15 , 0.3911891 , 0.0196338 , 0.4864018
5.20 , 0.3881793 , 0.0194842 , 0.5058860
5.25 , 0.3851305 , 0.0193327 , 0.5252187
5.30 , 0.3820409 , 0.0191793 , 0.5443980
5.35 , 0.3789088 , 0.0190237 , 0.5634217
5.40 , 0.3757324 , 0.0188660 , 0.5822878
5.45 , 0.3725096 , 0.0187060 , 0.6009938
5.50 , 0.3692384 , 0.0185437 , 0.6195375
5.55 , 0.3659168 , 0.0183789 , 0.6379164
5.60 , 0.3625424 , 0.0182115 , 0.6561279
5.65 , 0.3591128 , 0.0180414 , 0.6741693
5.70 , 0.3556256 , 0.0178685 , 0.6920377
5.75 , 0.3520781 , 0.0176926 , 0.7097303
5.80 , 0.3484676 , 0.0175136 , 0.7272440
5.85 , 0.3447910 , 0.0173315 , 0.7445754
5.90 , 0.3410454 , 0.0171459 , 0.7617213
5.95 , 0.3372273 , 0.0169568 , 0.7786782
6.00 , 0.3333333 , 0.0167640 , 0.7954422
6.05 , 0.3293598 , 0.0165673 , 0.8120095
6.10 , 0.3253026 , 0.0163666 , 0.8283761
6.15 , 0.3211578 , 0.0161615 , 0.8445376
6.20 , 0.3169208 , 0.0159520 , 0.8604895
6.25 , 0.3125868 , 0.0157377 , 0.8762272
6.30 , 0.3081507 , 0.0155184 , 0.8917457
6.35 , 0.3036072 , 0.0152939 , 0.9070396
6.40 , 0.2989504 , 0.0150639 , 0.9221035
6.45 , 0.2941740 , 0.0148281 , 0.9369317
6.50 , 0.2892713 , 0.0145861 , 0.9515178
6.55 , 0.2842351 , 0.0143377 , 0.9658554
6.60 , 0.2790577 , 0.0140823 , 0.9799378
6.65 , 0.2737306 , 0.0138197 , 0.9937575
6.70 , 0.2682447 , 0.0135494 , 1.0073069
6.75 , 0.2625901 , 0.0132709 , 1.0205777
6.80 , 0.2567563 , 0.0129837 , 1.0335614
6.85 , 0.2507314 , 0.0126872 , 1.0462486
6.90 , 0.2445029 , 0.0123809 , 1.0586294
6.95 , 0.2380569 , 0.0120640 , 1.0706934
7.00 , 0.2313782 , 0.0117359 , 1.0824293
7.05 , 0.2244501 , 0.0113957 , 1.0938250
7.10 , 0.2172543 , 0.0110426 , 1.1048676
7.15 , 0.2097706 , 0.0106756 , 1.1155433
7.20 , 0.2019764 , 0.0102937 , 1.1258369
7.25 , 0.1938471 , 0.0098956 , 1.1357325
7.30 , 0.1853547 , 0.0094800 , 1.1452126
7.35 , 0.1764684 , 0.0090456 , 1.1542581
7.40 , 0.1671534 , 0.0085905 , 1.1628487
7.45 , 0.1573707 , 0.0081131 , 1.1709618
7.50 , 0.1470760 , 0.0076112 , 1.1785730
7.55 , 0.1362192 , 0.0070824 , 1.1856553
7.60 , 0.1247429 , 0.0065241 , 1.1921794
7.65 , 0.1125815 , 0.0059331 , 1.1981125
7.70 , 0.0996594 , 0.0053060 , 1.2034185
7.75 , 0.0858889 , 0.0046387 , 1.2080572
7.80 , 0.0711674 , 0.0039264 , 1.2119836
7.85 , 0.0553748 , 0.0031636 , 1.2151472
7.90 , 0.0383685 , 0.0023436 , 1.2174908
7.95 , 0.0199785 , 0.0014587 , 1.2189495
8.00 , 0.0000000 , 0.0004995 , 1.2194489
F(8) - F(4) ≈ 1.219