Calculate the following integrals. If the answer requires a constant of integrat

Question

Calculate the following integrals. If the answer requires a constant of integration, enter it as c. You may enter a symbolic answer for any of the following (for some, that means a formula in terms of x, for others, that means a formula for the exact answer). For those integrals that have a numerical answer, you may enter the numerical value of the integral as a decimal, but be sure to enter sufficiently many decimal places (enter as many as you can). 4/x4 dx = 10 x5 dx = 31 (3/x + 5) dx = e-x/3 dx = 43 (5e-x/3 -2) dx = 5-x/x3 dx =

Explanation / Answer

i will write integration as I.
a) I(4/ x^4) = I(4 x^-4)= -4/3 (x^-3) + constant.
b) I(x^5) from x=0 to 1 = (x^6)/6 with limits from x=0 to 1 = 1/6.
c) I(3/x + 5 (x-1/2)) from x=1 to 3 = 3 lnx + (10 x1/2) with limits from x=1 to 3 =3(ln3) + 10(31/2-1)

d) I(e-x/3)= -3e-x/3 +constant

e)I(5e-x/3-2) from x=3 to 4 = -15e-x/3 -2x with limits from x=3 to 4 = -15(e-4/3-e-1) -2

f)I(-3/x1/2) = -6x1/2+constant

g)I((5-x)/x3) = I(5x-3) + I(-x-2) = -5/2 x-2 + x-1

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