Penjelasan dengan langkah-langkah:
integral tak tentu
[tex] \int \: ax {}^{n} \: dx = \frac{ {ax}^{n + 1} }{n + 1} + C \\ [/tex]
maka:
nomor (2)
[tex] \int \: 3 {x}^{2} \sqrt{ {x}^{3} } \: dx = \int \: 3 {x}^{2} \: . \: {x}^{ \frac{3}{2} } \: dx \\ \int \: 3 {x}^{2 + \frac{3}{2} } \: dx = \int3 {x}^{ \frac{7}{2} } \: dx \\ \frac{3 {x}^{ \frac{7}{2} + 1} }{( \frac{7}{2} + 1) } + C = \frac{3 {x}^{ \frac{9}{2} } }{( \frac{9}{2} )} + C \\ \frac{2}{9} \: . \: 3 {x}^{ \frac{9}{2} } + C = \frac{6}{9} {x}^{ \frac{9}{2} } + C = \frac{2}{3} {x}^{ \frac{9}{2} } + C[/tex]
nomor (3)
[tex] \int(x + 2) {}^{2} \: dx \\ [/tex]
misalkan:
[tex]u = x + 2 \to \: u' = 1[/tex]
[tex]dx = \frac{du}{ u' } = \frac{du}{1} = du \\ [/tex]
[tex] \int \: u {}^{2} \: dx = \int {u}^{2} \: . \: du \\ \frac{ {u}^{2 + 1} }{2 + 1} + C = \frac{1}{3} {u}^{3} + C \\ \frac{1}{3} (x + 2) {}^{3} + C[/tex]
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Verified answer
Penjelasan dengan langkah-langkah:
integral tak tentu
[tex] \int \: ax {}^{n} \: dx = \frac{ {ax}^{n + 1} }{n + 1} + C \\ [/tex]
maka:
nomor (2)
[tex] \int \: 3 {x}^{2} \sqrt{ {x}^{3} } \: dx = \int \: 3 {x}^{2} \: . \: {x}^{ \frac{3}{2} } \: dx \\ \int \: 3 {x}^{2 + \frac{3}{2} } \: dx = \int3 {x}^{ \frac{7}{2} } \: dx \\ \frac{3 {x}^{ \frac{7}{2} + 1} }{( \frac{7}{2} + 1) } + C = \frac{3 {x}^{ \frac{9}{2} } }{( \frac{9}{2} )} + C \\ \frac{2}{9} \: . \: 3 {x}^{ \frac{9}{2} } + C = \frac{6}{9} {x}^{ \frac{9}{2} } + C = \frac{2}{3} {x}^{ \frac{9}{2} } + C[/tex]
nomor (3)
[tex] \int(x + 2) {}^{2} \: dx \\ [/tex]
misalkan:
[tex]u = x + 2 \to \: u' = 1[/tex]
[tex]dx = \frac{du}{ u' } = \frac{du}{1} = du \\ [/tex]
[tex] \int \: u {}^{2} \: dx = \int {u}^{2} \: . \: du \\ \frac{ {u}^{2 + 1} }{2 + 1} + C = \frac{1}{3} {u}^{3} + C \\ \frac{1}{3} (x + 2) {}^{3} + C[/tex]