设t=x开6次方 x=t^6 dx=6t^5dt
∫dx/[(根号x)+x开3次方]
=∫6t^5dt/(t^3+t^2)
=6∫t^3dt/(t+1)
=6∫(t^3+1)dt/(t+1)-6∫dt/(t+1)
=6∫(t^2-t+1)dt-6ln|t+1|
=6(t^3/3-t^2/2+t)-6ln|t+1|+C
=2(x开平方)-3(x开3次方)+6(x开6次方)-6ln|x开6次方+1|+C
求不定积分∫dx/[(根号x)+x开3次方]
设t=x开6次方 x=t^6 dx=6t^5dt
∫dx/[(根号x)+x开3次方]
=∫6t^5dt/(t^3+t^2)
=6∫t^3dt/(t+1)
=6∫(t^3+1)dt/(t+1)-6∫dt/(t+1)
=6∫(t^2-t+1)dt-6ln|t+1|
=6(t^3/3-t^2/2+t)-6ln|t+1|+C
=2(x开平方)-3(x开3次方)+6(x开6次方)-6ln|x开6次方+1|+C