Re: [積分] 問一題積分∫x^0.5*e^x^0.5
※ 引述《otuse (pumacat)》之銘言：
: 請問要怎麼解阿~"~
√x
∫(√x)*(e ) dx
令 t = √x , 則 x = t^2 => dx = 2t dt
√x
∫(√x)*(e ) dx
t
= ∫(t)*(e )*(2t) dt
2 t
= (2)*(∫(t )*(e ) dt)
2 t t
= (2)*((t )*(e ) - ∫(e )*(2t) dt)
2 t t
= (2)*((t )*(e ) - (2)*(∫(t)*(e ) dt)
2 t t t
= (2)*((t )*(e ) - (2)*((t)*(e ) - ∫e dt))
2 t t t
= (2)*((t )*(e ) - (2)*((t)*(e ) - e )) + c
2 t t t
= (2)*(t )*(e ) - (4)*(t)*(e ) + (4)*(e ) + c
√x √x √x
= (2)*(x)*(e ) - (4)*(√x)*(e ) + (4)*(e ) + c
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