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Slove-xtanx-dx-




Question Number 22261 by tapan das last updated on 14/Oct/17
Slove  ∫xtanx dx
Slovextanxdx
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
usingintegrationbypartformulatosolveudv=uvvdusoletsmakeu=xdv=tanxdxdu=1dxv=lncosxsoweinputthevaluesxtanx=(x)(lncosx)lncosxdxxtanx=xlncosxlnsecx+c

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