A. ln 6 B. ln 7 C. ln 8 D. ln 9 E. 1

[tex]\text{Materi : Integral tertentu}\\\text{Kelas : XII SMA}\\\\\boxed{\boxed{\,\text{PEMBAHASAN}}}\\\\\int\limits^1_0 { \frac{x^7 - 1}{\text{In x}} } \, dx = \int\limits^1_0 { \frac{x^7}{\text{ln x}}- \frac{1}{\text{ln x}} } \, dx\\ \int\limits^1_0 { \frac{x^7 - 1}{\text{ln x}} } \, dx = \int\limits^1_0 { \frac{x^8}{\text{ln x}}. \frac{1}{x} } \, dx - \int\limits^1_0 { \frac{1}{\text{ln x}} } \, dx\\\\\text{Misal :}\\\text{ln x = u}\\ \frac{1}{\text{x}} \,\ dx = du\\\\[/tex]

[tex] \int\limits{ \frac{x^8}{\text{ln x}}. \frac{1}{x} } \, dx = \int\limits{ \frac{e^{8u}}{u} } \, du\\\\\text{Misal :}\\\text{8u = v}\\8\,\ du = dv \\\\ \int\limits{ \frac{x^8 }{\text{x}} . \frac{1}{x} } \, dx = \int\limits{ \frac{e^{8u}}{u} . \frac{8}{8} } \, du \\\int\limits{ \frac{x^8 }{\text{x}} . \frac{1}{x} } \, dx = \int\limits{ \frac{e^{8u}}{8u} . 8} \, du\\\int\limits{ \frac{x^8 }{\text{x}} . \frac{1}{x} } \, dx = \int\limits{ \frac{e^u}{u} } \, du\\[/tex]
[tex]\int\limits{ \frac{x^8 }{\text{x}} . \frac{1}{x} } \, dx = \text{E}_\text{i}(u)\\\int\limits{ \frac{x^8 }{\text{x}} . \frac{1}{x} } \, dx = \text{E}_\text{i}(8u)\\\int\limits{ \frac{x^8 }{\text{x}} . \frac{1}{x} } \, dx = \text{E}_\text{i}\text{(8ln x)}\\\int\limits{ \frac{1}{\text{ln x}}} \, dx = \text{li}(x)\\\\ \int\limits^1_0 { \frac{x^7 - 1}{ln x} } \, dx = \text{E}_\text{i}\text{(8ln x)} - \text{li}(x)\text{l} \right^1_0\\\boxed{\boxed{\int\limits^1_0\frac{x^7 - 1}{\ln x}\, dx= \ln8}}[/tex]

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