5. Evaluate the following using integration by parts:
(a) â« x sin(3x) dx
(b) 3 â«1 lnx dx
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Use Integration by parts to find the indefinite integral:
1. Integrand (x^2 * e^-x * dx)
2. Integrand (x^2 * e^2x * dx)
3. Integrand (squareroot x * lnx * dx)
1. Evaluate using integration by parts.
Integral 3xsqrt(3x-10) dx
a. 2/3 x(3x-10)^3/2 - 4/15(3x-10)^5/2 + C
b. 2/3 x(3x-10)^3/2 - 4/45(3x-10)^5/2 + C
c. x(3x-10)^3/2 - 4/15(3x-10)^5/2 + C
d. 2/3 x(3x-10)^3/2 + 4/45(3x-10)^5/2 + C
2. Evaluate using integration by parts.
Integral ^(x-8) e4x dx
a. 4(x-8)e^4x â 16e^4x + C
b. ¼(x-8)e^4x + 1/16e^4x +C
c. ¼(x-8)e^4x - 1/16e^4x +C d. (x-8)e^4x - e^4x +C