Question

integral of dx/ x+sqrt(1+2x)?

Answer 1

\[\int\limits_{}^{} \frac{ dx }{ x+\sqrt{1+2x} }\]

Answer 2

trig or algebraic?

Answer 3

you might try using the substitution u = 1+ 2x

Answer 4

means algebraic?

Answer 5

yes

Answer 6

u^2 = 1+2x may also work out nicely

Answer 7

yes - thats better - what @ganeshie8 said

Answer 8

\[u=\sqrt{1+2x}\]
\[u ^{2}=1+2x\]
\[x=\frac{ u ^{2}-1 }{ 2 }\]

Answer 9

thats the way to go

Answer 10

now find dx

Answer 11

in terms of du

Answer 12

so,\[dx=\frac{ 1 }{ 2} 2u\]
dx=u?
then
\[\frac{ u }{ \frac{ u ^{2-1} }{ 2 } +u}\]

Answer 13

no dx = u du

Answer 14

ya..thats how it is i forgot du...nut am i doing it right in terms of substituting?

Answer 15

*nut=but

Answer 16

yes

we have