Evaluate the following integral ∫x^3/(2+3x)^4 dx
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total answers (1)
total answers (1)
Mathematics
Put x=(u-2)/3 and dx=1/3 du
need an explanation for this answer? contact us directly to get an explanation for this answer∫x^3/(2+3x)^4 dx=1/81 ∫(u-2)^3/u^4 du
=1/81 ∫(u^3-6u^2+12u-8)/u^4 du
=1/81 ∫1/u-6/u^2 +12/u^3 -8/u^4 du
=1/81 [lnu+6/u-6/u^2 +8/(3u^3 )]+c
=1/81 [ln〖(2+3x)+6/(2+3x)-6/(2+3x)^2 +8/(3(2+3x)^3 )〗 ]+c