求下列不定积分:)积分号[(x^2+根号下x^3+3x)/根号下x]dx;2)积分号[sin(x/2)]^2dx;
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积分号[(x^2+根号下x^3+3x)/根号下x]dx
=∫[x^(3/2)+x+3x^(1/2)]dx
=(2/5)x^(5/2)+x^2/2+2x^(3/2)+C.
积分号[sin(x/2)]^2dx
=∫[1/2-(cosx)/2]dx
=x/2-(sinx)/2+C
积分号[cos2x/(cosx+sinx)]dx
=∫[cosx-sinx]dx
=sinx+cosx+C.
积分号[(x^3-27)/(x-3)]dx
=∫[x^2+3x+9]dx
=x^3/3+3x^2/2+9x+C.
=∫[x^(3/2)+x+3x^(1/2)]dx
=(2/5)x^(5/2)+x^2/2+2x^(3/2)+C.
积分号[sin(x/2)]^2dx
=∫[1/2-(cosx)/2]dx
=x/2-(sinx)/2+C
积分号[cos2x/(cosx+sinx)]dx
=∫[cosx-sinx]dx
=sinx+cosx+C.
积分号[(x^3-27)/(x-3)]dx
=∫[x^2+3x+9]dx
=x^3/3+3x^2/2+9x+C.
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