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