[tex] \displaystyle \int \sf(2x \sqrt{x} - \frac{2x}{ \sqrt{x} }) \: \: dx = ..[/tex]
Pembahasan :
[tex]\displaystyle \sf \int 2x \sqrt{x } - \frac{2x}{ \sqrt{x} } \: dx[/tex]
[tex] = \displaystyle \sf \int 2x.x {}^{ \frac{1}{2} } - 2 \sqrt{x} \: dx[/tex]
[tex] = \displaystyle \sf \int 2x {}^{ \frac{3}{2} } - 2x {}^{ \frac{1}{2} } \: dx[/tex]
[tex] = \displaystyle \sf \int 2x {}^{ \frac{3}{2} } \: dx - \displaystyle \sf \int 2x {}^{ \frac{1}{2} } \: dx[/tex]
[tex] = \frac{4x {}^{2} \sqrt{x} }{5} - \frac{4x \sqrt{x} }{3} [/tex]
[tex] = \frac{4x {}^{2} \sqrt{x} }{5} - \frac{4x \sqrt{x} }{3} + C[/tex]
[tex]\displaystyle \int \sf(2x \sqrt{x} - \frac{2x}{ \sqrt{x} }) \: \: dx[/tex]
[tex]\displaystyle = \int \sf (2 {x}^{ \frac{3}{2} } - 2 {x}^{ \frac{1}{2} } ) \: \: dx[/tex]
[tex] \sf = \dfrac{2 {x}^{ \frac{3}{2} + 1} }{ \frac{3}{2} + 1 } - \dfrac{2 {x}^{ \frac{1}{2} + 1} }{ \frac{1}{2} + 1 } + C[/tex]
[tex] \sf = \dfrac{2 {x}^{ \frac{5}{2} } }{ \frac{5}{2} } - \dfrac{2 {x}^{ \frac{3}{2} } }{ \frac{3}{2} } + C[/tex]
[tex] \sf = \dfrac{4 {x}^{ \frac{5}{2} } }{ 5 } - \dfrac{4 {x}^{ \frac{3}{2} } }{ 3} + C[/tex]
[tex] \sf = \dfrac{4 \sqrt{ {x}^{5} } }{ 5 } - \dfrac{4 \sqrt{ {x}^{3} } }{ 3} + C[/tex]
[tex] \boxed{ \sf = \dfrac{4 {x}^{2} \sqrt{ {x}} }{ 5 } - \dfrac{4x \sqrt{ {x} } }{ 3} + C}[/tex]
[answer.2.content]
