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Slove-xtanx-dx-




Question Number 22261 by tapan das last updated on 14/Oct/17
Slove  ∫xtanx dx
$$\mathrm{Slove} \\ $$$$\int\mathrm{xtanx}\:\mathrm{dx} \\ $$
Answered by scottfeed last updated on 13/Nov/17
using integration by part formula to solve               ∫udv=uv−∫vdu  so lets make u=x      dv=∫tanx dx                                du=1dx       v= −ln∣cosx∣  so we input the values         ∫xtanx=(x)(−ln∣cosx∣)−∫−ln∣cosx∣dx         ∫xtanx=−xln∣cosx∣ −ln∣secx∣+c
$${using}\:{integration}\:{by}\:{part}\:{formula}\:{to}\:{solve} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int{udv}={uv}−\int{vdu} \\ $$$${so}\:{lets}\:{make}\:{u}={x}\:\:\:\:\:\:{dv}=\int{tanx}\:{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{du}=\mathrm{1}{dx}\:\:\:\:\:\:\:{v}=\:−{ln}\mid{cosx}\mid \\ $$$${so}\:{we}\:{input}\:{the}\:{values} \\ $$$$\:\:\:\:\:\:\:\int{xtanx}=\left({x}\right)\left(−{ln}\mid{cosx}\mid\right)−\int−{ln}\mid{cosx}\mid{dx} \\ $$$$\:\:\:\:\:\:\:\int{xtanx}=−{xln}\mid{cosx}\mid\:−{ln}\mid{secx}\mid+{c} \\ $$$$ \\ $$

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