\( \int x\left(\frac{\ln a^{a^{x / 2}}}{3 a^{5 x / 2} b^{3 x}}+\frac{\ln b^{b^{x}}}{2 a^{2 x} b^...
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0\( \int x\left(\frac{\ln a^{a^{x / 2}}}{3 a^{5 x / 2} b^{3 x}}+\frac{\ln b^{b^{x}}}{2 a^{2 x} b^{4 x}}\right) d x \) (where \( \left.a, b \in R^{+}\right) \)is equa to
(A) \( \frac{1}{6 \ln a^{2} b^{3}} a^{2 x} b^{3 x} \ln \frac{a^{2 x} b^{3 x}}{e}+k \)
(B) \( \frac{1}{6 \ln a^{2} b^{3}} \frac{1}{a^{2 x} b^{3 x}} \ln \frac{1}{e a^{2 x} b^{3 x}}+k \)
(C) \( \frac{1}{6 \ln a^{2} b^{3}} \frac{1}{a^{2 x} b^{3 x}} \ln \left(a^{2 x} b^{3 x} e\right)+k \)
(D) \( -\frac{1}{6 \ln a^{2} b^{3}} \frac{1}{a^{2 x} b^{3 x}} \ln \left(a^{2 x} b^{3 x} e\right)+k \)
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