Calculus

1.evaluate (integral sign)x cos 3x dx
A.1/6 x^2 sin 3x + C
B.1/3 x sin 3x -1/2 sin 3x +C
C.1/3 x sin 3x +1/9 cos 3x +C << my choice.
D. 1/2 x^2 +1/18 sin^2 3x +C

2.evaluate (integral sign)xe(power of 2x)dx
A.1/6 x^2 e(to the power of 3x)+C

B.1/2 xe(to the power of 2x)-1/2 e(to
the power of 2x)+C

C.1/2xe(to the power of 2x) -1/4 e(to the power of 2x) +C

D.1/2 x^2 -1/8 e(to the power of 4x +C

I don't know the answer to this one.

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  1. 1. C is Correct
    Integration by parts,
    ∫xcos(3x)dx
    =(1/3)xsin(3x)-(1/3)∫cos(3x)dx
    = ....

    2. Same as 1. Use integration by parts

    ∫xe2xdx
    =(1/2)xe2x-(1/2)∫e2xdx
    =...

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  2. C ?

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  3. Perfect!

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