Menu Close

x-x-2-1-4-dx-




Question Number 6959 by Tawakalitu. last updated on 03/Aug/16
∫ x (x + 2)^(1/4)  dx
$$\int\:{x}\:\left({x}\:+\:\mathrm{2}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:{dx}\: \\ $$
Answered by FilupSmith last updated on 03/Aug/16
u=x+2  x=u−2  du=dx  =∫(u−2)u^(1/4) du  =∫(u^(5/4) −2u^(1/4) )du  (4/9)u^(9/4) −2u^(5/4) +c  (4/9)(x+2)^(9/4) −2(x+2)^(5/4) +c
$${u}={x}+\mathrm{2} \\ $$$${x}={u}−\mathrm{2} \\ $$$${du}={dx} \\ $$$$=\int\left({u}−\mathrm{2}\right){u}^{\mathrm{1}/\mathrm{4}} {du} \\ $$$$=\int\left({u}^{\mathrm{5}/\mathrm{4}} −\mathrm{2}{u}^{\mathrm{1}/\mathrm{4}} \right){du} \\ $$$$\frac{\mathrm{4}}{\mathrm{9}}{u}^{\mathrm{9}/\mathrm{4}} −\mathrm{2}{u}^{\mathrm{5}/\mathrm{4}} +{c} \\ $$$$\frac{\mathrm{4}}{\mathrm{9}}\left({x}+\mathrm{2}\right)^{\mathrm{9}/\mathrm{4}} −\mathrm{2}\left({x}+\mathrm{2}\right)^{\mathrm{5}/\mathrm{4}} +{c} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *