∫x171+x18dxTake 1+x18=t18x17dx=dtx17dx=dt18=∫dt18t=118log|t|+c⇒118log|1+x18|+c

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$\int \frac{x^{17}}{1 + x^{18}} d x =$

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$\frac{1}{17} \log | 1 + x^{17} | + c$

$\frac{1}{18} \log | 1 + x^{18} | + c$

$\frac{1}{15} \log | 1 + x^{15} | + c$

$\frac{1}{16} \log | 1 + x^{16} | + c$

answer is A.

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Detailed Solution

$\int \frac{x^{17}}{1 + x^{18}} d x$

Take $1 + x^{18} = t$

$18 x^{17} d x = d t$

$x^{17} d x = \frac{d t}{18}$

$= \int \frac{d t}{18 t}$

$= \frac{1}{18} \log | t | + c$

$\Rightarrow \frac{1}{18} \log | 1 + x^{18} | + c$

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