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Instituto Tecnologico Superior de Alamo-TemapacheIntegral Calculus - Homework 2.3M.C. Liliana Guadalupe Salvador
Deadline: March 25, 2014
1. Read the section 2.3 in the Zill’s book.
2. Evaluate the integral using integration by parts with the indicated choices of u anddv
a)∫x ln(x) dx; u = ln(x), dv = x
b)∫ln(x) dx; u = ln(x), dv = 1
c)∫t cos(t) dt; u = t, dv = cos(t)
d)∫x√x+ 3 dx; u = x, dv =
√x+ 3
e)∫
x√x+1
dx; u = x, dv = 1√x+1
;
3. Use integration by parts to proof the integral.
a)∫z3 ln(z) dz = 1
4z4 ln(z)− 1
16z4 + C
b)∫x ln(2x) dx = 1
2x2 ln(2x)− 1
2x2 + C
c)∫xe3x dx = 1
3xe3x − 1
9e3x + C
d)∫t sec2(t) dt = x tan(t)− ln | sec(t)|+ C
4. Evaluate the integral using integration by parts.
a)∫z2 ln(z) dz
b)∫x1/2 ln(x) dx
c)∫ln(4z) dz
d)∫t sen(4t) dt
e)∫x4 ln(x) dx
f )∫x√x+ 2 dx
g)∫t sin(1− 2t) dt
h)∫xe2x dx
i)∫
x√2x−5 dx
j )∫x2 cos(3x) dx
k)∫x tan2(x) dx
l)∫t sec(t) tan(t) dt