PART 9：例題-快速解積分(1)(求不定積分)

\(\int {\frac{{{x^9}}}{{{x^{10}} + 7}}\;dx} \)

SOL:

(下= \({x^{10}} + 7\) ，下的微分= \(10{x^9}\)，與上面相同多10倍)

\(\int {\frac{{{x^9}}}{{{x^{10}} + 7}}\;dx} \) \( = \frac{1}{{10}}\int {\frac{{10{x^9}}}{{{x^{10}} + 7}}\;dx}  = \frac{1}{{10}}\ln ({x^{10}} + 7) + C\) \( = \frac{1}{2}{\left( {\ln x} \right)^2} + C\)