Merge remote-tracking branch 'origin/develop' into develop

素材/整合素材/高数素材/不定积分大集合——技巧篇.md

@@ -26,9 +26,10 @@ $$\int \frac{1}{(x^2+1)\sqrt{x^2-1}} dx$$
 $$\begin{align*}
 \int \frac{1}{(x^2+1)\sqrt{x^2-1}} dx &= \int \frac{\sec t \tan t}{(\sec^2 t+1)\tan t} dt \\
 &= \int \frac{\cos t}{\cos^2 t+1} dt \\
-&= \arctan(\sin t) + C \\
-&= \arctan\left(\frac{\sqrt{x^2-1}}{x}\right) + C
-\end{align*}$$
+
+&=  \frac{1}{2\sqrt{2}} \ln\left| \frac{\sqrt{x^2-1} + x\sqrt{2}}{\sqrt{x^2-1} - x\sqrt{2}} \right| + C\\
+\end{align*}\\
+$$
 【2.2】
 
 $$\int \frac{1}{x\sqrt{x^2-1}} dx$$