Tolong bantu saya kak, tugasnya bentar lagi harus di kumpul hari ini juga. Beserta cara ya kak.

Tolong bantu saya kak, tugasnya bentar lagi harus di kumpul hari ini juga. Beserta cara ya kak.

Penjelasan dengan langkah-langkah:

37)

misal

$u = {x}^{2} + 1 \ du = 2x : dx \ dx = frac{du}{2}$

$int{u}^{3} (2x) frac{du}{2x} \ = int {u}^{3} du \ = frac{1}{3 + 1} {u}^{3 + 1} + c \ = frac{1}{4} {u}^{4} + c \ = frac{1}{4} ( {x}^{2} + {1)}^{4} + c$

38)

misal

$u = {x}^{3} - 2 \ du = 3 {x}^{2} dx \ dx = frac{du}{3 {x}^{2} }$

$int 6 {x}^{2} ( {u}^{ - 3} ) frac{du}{3 {x}^{2} } \ = int 2 {u}^{ - 3} du \ = frac{2}{ - 3 + 1} {u}^{ - 3 + 1} +c \ = - frac{2}{2} {u}^{ - 2} + c \ = - frac{1}{{u}^{2} } + c \ = - frac{1}{( { {x}^{3} - 2})^{2} } + c$

39)

misal

$u = 1 + 3 {x}^{2} \ du = 6x : dx \ dx = frac{du}{6x}$

$int 2x( {u}^{ frac{1}{2} } ) frac{du}{6x} \ = int frac{1}{3} {u}^{ frac{1}{2} } du \ = frac{1}{3}( frac{ {u}^{ frac{1}{2} + frac{2}{2} } }{ frac{1}{2} + frac{2}{2} } ) + c \ = frac{1}{3} ( frac{ {u}^{ frac{3}{2} } }{ frac{3}{2} } ) + c \ = frac{1}{3} ( frac{2}{3} ) sqrt{( {1 + 3 {x}^{2} })^{3} } + c \ = frac{2}{9} sqrt{(1 + 3 {x}^{2} ) ^{3} } + c$

40)

$u = {x}^{3} + 2 \ du = 3 {x}^{2} dx \ dx = frac{du}{3 {x}^{2} }$

$= int {u}^{2} (3 {x}^{2} ) frac{du}{3 {x}^{2} } dx \ = int {u}^{2} du \ = frac{ {u}^{3} }{3} + c \ = frac{1}{3} ( { {x}^{3} + 2 })^{3} + c$

41)

$u = {x}^{3} + 2 \ du = 3 {x}^{2} dx \ dx = frac{du}{3 {x}^{2} }$

$= int 8 {x}^{2} {u}^{ - 3} frac{du}{3 {x}^{2} } \ = frac{8}{3} ( frac{ {u}^{ - 2} }{ - 2} ) + c \ = - frac{4}{3 {u}^{2} } + c \ = - frac{4}{3{( {x}^{3} + 2 })^{2}} + c$