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Calc 2 6.1

 

<== Calculus 2
Number Question Answer
See the work

1.

 

 

Use integration by parts          
to evaluate the integral
∫ xe^(4x)dx

 

(1/4)(xe^(4x)-(1/4)e^(4x))+C

 

The work

Point Cost: 3

2.

 

 

Use integration by parts 
to evaluate the integral 
∫ 5xcos(2x)dx

 

5*0.5*(xsin(2x)+0.5*cos(2x))+C

 

The work

Point Cost: 3

3.

 

 

Use integration by parts 
to evaluate the integral 
∫ ln(7x+8)dx

 

ln(7x+8)x+(8ln(7x+8))/7+C

 

The work

Point Cost: 3

4.

 

 

Use integration by parts 
to evaluate the integral 
∫ arctan(8t)dt

 

t*arctan(8t)-(1/16)(ln(1+8t)^2)+C
The work

Point Cost: 3

5.

 

Evaluate the indefinite integral
∫ e^(3x)sin(2x)dx

 

(-2/13)(e^(3x))cos(2x))+(3/13)(e^(3x)sin(2x))+C 
The work

Point Cost: 4

6.

 

 

Evaluate the integral
a= 3
b=1
∫ lnx/x^8

 

.0203270691748022

The work

Point Cost: 3

7.

 

 

 

 

Use integration by parts 
to evaluate the integral 

a= 2

b= 1

∫ sqrt(t)lnt dt

 

0.4943765803
The work

Point Cost: 3

8.

 

 

Use integration by parts 
to evaluate the integral 
∫ (ln(4x))^2 dx

 

x(ln(4x))^2-2xln(4x)+2x+C
The work

Point Cost: 3

9.

 

Evaluate the integral

a= 10

b=8

∫arctan(8x) dx

 

1.45557
The work

10.

 

 

 

 

First make a substitution and then use
integration by parts to evaluate the 
integral

∫ (x^5)cos(x^3)dx

 

 

(1/3)(x^3)(sin(x^3)+(1/3)(cos(x^3))+C
The work

Point Cost: 3

11.

 

Use integration by parts 
to evaluate the integral 

a=9

b=1

∫ e^(6*)

 

62012081.015917
The work