1.

Integration of (1/2-3x)+1/√(3x-2) dx

Answer»

ANSWER:

dx1+3x2

SUBSTITUTE:

x=13√tanu

dx=13√sec2udu

∫13√sec2udu1+3(13√tanu)2

Pull out that constant:

13–√∫sec2udu1+3(13tan2u)

Do the math:

13–√∫sec2udu1+tan2u

Trigonometric IDENTITY: 1+tan2u=sec2u:

13–√∫sec2udusec2u

Cancel:

13–√∫du

That LOOKS PRETTY easy:

13–√u+C

Undo the substitution:

13–√arctan(3–√x)+C

Check the answer on desmos:


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