evaluate the integral.\n int\frac{dx}{sqrt{121 + x^{2}}}\n int\frac{dx}{sqrt{121 + x^{2}}}=square\n(type an…
evaluate the integral.\n int\frac{dx}{sqrt{121 + x^{2}}}\n int\frac{dx}{sqrt{121 + x^{2}}}=square\n(type an exact answer, using radicals as needed.)
Answer
Explanation:
Step1: Recall integral formula
We know that $\int\frac{dx}{\sqrt{a^{2}+x^{2}}}=\ln|x + \sqrt{x^{2}+a^{2}}|+C$. Here $a^{2}=121$, so $a = 11$.
Step2: Apply the formula
Substituting $a = 11$ into the formula, we get $\int\frac{dx}{\sqrt{121+x^{2}}}=\ln|x+\sqrt{x^{2}+121}|+C$.
Answer:
$\ln|x+\sqrt{x^{2}+121}|+C$