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(3)
∫1/[x²√x]dx
=∫x^(-5/2)dx
=-⅔x^(-3/2) +C
(7)
∫[(x-1)³/x²]dx
=∫[(x³-3x²+3x-1)/x²]dx
=∫(x -3 +3/x -1/x²)dx
=½x²-3x +3ln|x| + 1/x +C
(9)
∫[x²/(x²+1)]dx
=∫[(x²+1-1)/(x²+1)]dx
=∫[1- 1/(x²+1)]dx
=x- arctanx +C
(17)
∫secx(secx-tanx)dx
=∫(sec²x-secxtanx)dx
=tanx-secx +C
∫1/[x²√x]dx
=∫x^(-5/2)dx
=-⅔x^(-3/2) +C
(7)
∫[(x-1)³/x²]dx
=∫[(x³-3x²+3x-1)/x²]dx
=∫(x -3 +3/x -1/x²)dx
=½x²-3x +3ln|x| + 1/x +C
(9)
∫[x²/(x²+1)]dx
=∫[(x²+1-1)/(x²+1)]dx
=∫[1- 1/(x²+1)]dx
=x- arctanx +C
(17)
∫secx(secx-tanx)dx
=∫(sec²x-secxtanx)dx
=tanx-secx +C
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