Evaluate the indefinite integral. integrate of ln(x^2+10x+24)dx
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You need to use integration by parts such that:
`int udv = uv - int vdu`
Considering `u = ln(x^2+10x+24)` and `dv = dx` yields:
`u = ln(x^2+10x+24) => du = (2x+10)/(x^2+10x+24) dx`
`dv = dx => v = x`
`int ln(x^2+10x+24)dx = xln(x^2+10x+24) - int (2x^2 + 10x)/(x^2+10x+24) dx`
Using reminder theorem yields:
`(2x^2 + 10x) = 2(x^2+10x+24) - 10x`
`(2x^2 + 10x)/(x^2+10x+24) = 2 - 10x/(x^2+10x+24)`
Integrating both sides yields:
`int (2x^2 + 10x)/(x^2+10x+24) dx= int2 dx- int 10x/(x^2+10x+24) dx`
`int (2x^2 + 10x)/(x^2+10x+24) dx = 2x - 10 int x/(x^2+10x+24) dx`
You need to come up with the substitution...
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