Đặt [tex]\frac{1}{x^{2}}=t[/tex][tex]\Rightarrow \frac{-2}{x^{3}}dx=dt\Rightarrow \int \frac{1}{x^{7}-10x^{3}}dx=\int \frac{1}{x^{3}(x^{4}-10)}dx=-\frac{1}{2}\int \frac{1}{\frac{1}{t^{2}}-10}dt=-\frac{1}{2}\int \frac{t^{2}}{1-10t^{2}}dt[/tex] [tex]=-\frac{1}{2}\int (-\frac{1}{10}+\frac{1}{10(1-10t^{2})})dt=\frac{1}{20}\int dt-\frac{1}{20}\int \frac{1}{(1-\sqrt{10}t)(1+\sqrt{10}t)}dt=\frac{1}{20}t-\frac{1}{40\sqrt{10}}.ln\left | \frac{1+\sqrt{10}t}{1-\sqrt{10}t} \right |+C=\frac{1}{20x^{2}}-\frac{1}{40\sqrt{10}}.ln\left | \frac{x^{2}+\sqrt{10}}{x^{2}-\sqrt{10}} \right |+C[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
