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The induced emf in a 5-henry inductor varies as V=(6t+26)/(t^2+10t+21). Recalling that current i=1/L∫Vdt, find the formula for the current i as a function of time t.

This is what I've gotten so far...

∫(6t+26)/(t^2+10t+21)=(6t+26)/(t+3)(t+7)=A/(t+3)+B(t+7)=2/(t+3)+4/(t+7) dt

i=1/5∫2/(t+3)+4/(t+7)dt

i=1/5(ln(t+3)^2+ln(t+7)^4+k...

Well should I stop here since I've gotten only the variable t on the right side of the formula or should differentiate it since they are asking for the formula of currentas a function of time t? If so... is this correct?

di/dt=1/5{[(2t+6)/(t+3)^2]+[(4t+28)/(t+7)^4)]}

Thank you again guys...