Calc simple indefinite indefinite integrals help?

Question

evaluate the following indefinite integrals Without using substitution.

a) ∫ x^2+4x+3/ √x dx

b) ∫ e/ 2x^2 dx

c) ∫ 3e^t/2 dt

Answer 1

The point of these problems is to simplify expressions in the integrand and move constants to the outside of the integral sign.

a) ∫ x^2+4x+3/ √x dx

= ∫ [ x^(3/2) + 4*x^(1/2) +3*x^(-1/2) ] dx

= [ ∫ x^(3/2) dx ] + [ 4 * ∫ x^(1/2) dx ]  + [ 3 * ∫ x^(-1/2) dx ]

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b) ∫ e/ 2x^2 dx = (e/2) * ∫ x^2 dx

{ e is just a constant in this integral }

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c) ∫ 3e^t/2 dt = (3/2) * ∫ e^t dt

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These are straightforward integrals from this point.