求不定积分∫[1/(5x+1)根号( ln(5x+1))]dx=.=式子不好打.大家将就着看吧...1楼的算完了??

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求不定积分∫[1/(5x+1)根号(ln(5x+1))]dx=.=式子不好打.大家将就着看吧...1楼的算完了??求不定积分∫[1/(5x+1)根号(ln(5x+1))]dx=.=式子不好打.大家将就

求不定积分∫[1/(5x+1)根号( ln(5x+1))]dx=.=式子不好打.大家将就着看吧...1楼的算完了??
求不定积分∫[1/(5x+1)根号( ln(5x+1))]dx
=.=式子不好打.大家将就着看吧
...1楼的算完了??

求不定积分∫[1/(5x+1)根号( ln(5x+1))]dx=.=式子不好打.大家将就着看吧...1楼的算完了??
∫dx/{(5x+1)[In(5x+1)]^(1/2)}
=(1/5)∫d(5x+1)/{(5x+1)[In(5x+1)]^(1/2)}
=(1/5)∫d[In(5x+1)]/[In(5x+1)]^(1/2)
=(2/5)[In(5x+1)]^(1/2)+C

逆用换元积分法啊!令u=ln(5x+1),则1/(5x+1)=u'
所以原式等于∫[u'乘以根号(1/u)]dx
=∫根号(1/u)du
=2(根号u)+C
再把u=In(5x+1)代回去,
2(根号u)+C
=2根号[In(5x+1)]+C
不知道算得对不对啊