hey can someone help me with some calculus?
im having alot of trouble with this stuff can anyone help me with any of these problems?
integrate by parts: x^2 e^3x dx
integrate by parts:ln(x^2+1)dx
integrate by parts:cos^23x dx
integrate by parts:tan^2x/secx dx
integrate by parts:dx/(4-x^2)^3/2 dx
integrate by parts: 1/square root of (x^2+4x+5) dx
integrate by parts:9/(x+2)^2(1-x) (i think this one uses partial fraction decomposition.
integration tables for this one: square root of 3+2x-x^2 all dived by (x-1)^2
finally, integrate from 1 to 5 x/square root of 5-x and i need to know if it diverges or not (the graph)
if anyone can do any of these for me that would be most appreciated
i gotta be honest...im really terrible with this stuff...like i get integrating, and i could do force problems and planar lamina no problem...but this stuff just kills me, can you show me like through and through how to do atleast one? id be eternally greatful 
I'll set you up for some of these.
∫ u dv = uv - ∫ v du
#1) u = x², du = 2x dx, dv = e^(3x) dx, v = 1/3e^(3x)
∫ u dv = uv - ∫ v du
∫ x²e^(3x) dx = x²*1/3e^(3x) - ∫ 1/3e^(3x) * 2x dx
∫ x²e^(3x) dx = 1/3x²*e^(3x) - 2/3∫ e^(3x)x dx
Do another integration by parts for the integral ∫e^(3x)x dx
u = x, du = dx, dv = e^(3x), v = 1/3e^(3x)
∫e^(3x)x dx = 1/3*xe^(3x) - ∫ 1/3e^(3x) dx
∫e^(3x)x dx = 1/3*xe^(3x) - 1/9e^(3x)
Substitute this for the remaining integral from the 1st integration by parts:
∫ x²e^(3x) dx = 1/3x²*e^(3x) - 2/3∫ e^(3x)x dx
∫ x²e^(3x) dx = 1/3x²*e^(3x) - 2/3[1/3*xe^(3x) - 1/9e^(3x)]
∫ x²e^(3x) dx = 1/3x²*e^(3x) - 2/9*xe^(3x) + 2/27e^(3x) + C
#2) u = ln(x²+1), du = 2x/(x²+1) dx, dv = dx, v = x
#3) u = cos²(3x), du = -6cos(3x)sin(3x), dv = dx, v = x
#4) Not sure how to do this by parts. I would use the identity sec²(x) - 1 = tan²(x) to get ∫[sec²(x) - 1]/sec(x) dx = ∫sec(x) - cos(x) dx
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