How do you integrate $int sqrt(1+2x)$ using substitution?

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How do you integrate $int sqrt(1+2x)dx$ using substitution?

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Answer 1 · 2016-09-09T21:10:41

$1/3(sqrt(1+2x))^3+C, or$

$1/3(1+2x)^(3/2)+C$ .

We subst. $1+2x=t^2" in "I=intsqrt(1+2x)dx$ .

$:. 2dx=2tdt, or, dx=tdt$ . Also, $sqrt(1+2x)=t$

Therefore, $I=intt*tdt=intt^2dt=t^3/3$

$=1/3(sqrt(1+2x))^3+C, or$

$intI=1/3(1+2x)^(3/2)+C$ .