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**shadow85** 1. Calculate the integrals of:

a*x*sin(bx) dx

Mr F says: Use integration by parts.

and

(x^2)(sin^2(ax)) dx

where a and b are constants. hint: use double angle formula

Mr F says: $\displaystyle {\color{red}\sin^2 (ax) = \frac{1}{2} \left( 1 - \cos (2ax) \right)}$.

Hint 2: Use integration by parts (twice).

2. consider the improper integral

integral from (2*sqrt(3)) to infiniti of: (24x^3)/(4+x^2)^(5/2) dx.

EDIT: Make an appropriate trigonometric substitution to convert into a proper integral. Hence determine its value.

Mr F says: Substitute $\displaystyle {\color{red} x = 2 \tan t}$.

Someone can help me with these please?