Question

Find the intergral using U substitution

Answer 1

\[\int\limits_{0}^{1}((dx)/(1+\sqrt{x}))^4\]

Answer 2

put u= 1+\(\sqrt x\)
du=.... ?

Answer 3

before finding, du, find x= ... ? in terms of u.

Answer 4

if you make \[1+\sqrt{x}\] U then
Du=\[\frac{ 1 }{ 2\sqrt{x}}\]

but it doesnt fit. in \[\int\limits_{0}^{1} \frac{ dx} { u^4 }\]

Answer 5

you still have a \[\frac{1}{dx}\] that Du needs to be equal to

Answer 6

?

Answer 7

that was the reason i asked you to 'before finding, du, find x= ... ? '
so,
x= (u-1)^2
now differentiate.
dx = 2 (u-1) du
so, now what will your integral become ??