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dx-x-x-1-4-1-10-




Question Number 79612 by john santu last updated on 26/Jan/20
∫ (dx/( (√(x ))((x)^(1/(4 )) +1)^(10) )) = ?
dxx(x4+1)10=?
Answered by MJS last updated on 26/Jan/20
∫(dx/(x^(1/2) (x^(1/4) +1)^(10) ))=       [t=x^(1/4)  → dx=4x^(3/4) dt]  =4∫(t/((t+1)^(10) ))dt=4∫(dt/((t+1)^9 ))−4∫(dt/((t+1)^(10) ))=  =−(1/(2(t+1)^8 ))+(4/(9(t+1)^9 ))=−((9t+1)/(18(t+1)^9 ))=  =−((9x^(1/4) +1)/(18(x^(1/4) +1)^9 ))+C
dxx12(x14+1)10=[t=x14dx=4x34dt]=4t(t+1)10dt=4dt(t+1)94dt(t+1)10==12(t+1)8+49(t+1)9=9t+118(t+1)9==9x14+118(x14+1)9+C
Commented by peter frank last updated on 26/Jan/20
thanks
thanks
Commented by john santu last updated on 27/Jan/20
thank you mister
thankyoumister

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