Xét [tex]I=\int f(x)dx=\int \dfrac{x}{cos^2x}dx\Rightarrow \left\{\begin{matrix} u=x & \\ dv=\dfrac{1}{cos^2x}dx & \end{matrix}\right.\Rightarrow \left\{\begin{matrix} du=dv & \\ v=tanx & \end{matrix}\right.[/tex]
[tex]\Leftrightarrow I=x.tanx-\int tanxdx=x.tanx+ln|cosx|+C[/tex]
[tex]F(x)=\int x.f'(x)dx \Rightarrow \left\{\begin{matrix} u=x & \\ dv=f'(x)dx & \end{matrix}\right.\Rightarrow \left\{\begin{matrix} du=dx & \\ v=f(x) & \end{matrix}\right.[/tex]
[tex]\Rightarrow F(x)=x.f(x)-\int f(x)dx=x.f(x)-x.tanx-ln|cosx|+C[/tex]
Thay [tex]x=0\Rightarrow C=0[/tex]
[tex]\Rightarrow F(x)=\dfrac{x^2}{cos^2x}-x.tanx-ln|cosx|[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
