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Calc 2 6.3

 

<== Calculus 2
Number Question Answer
See the work

1.

 

 

 

The partial fraction decomposition of (x^2+70)/(x^3+x^2)
can be written in the form of ƒ(x)/x+g(x)/x^2+h(x)/(x+1),       
where
f(x)=_______
g(x)=________
h(x)=________

 

f(x)=-70
g(x)=70
h(x)=71
The work

Point Cost: 3

2.

 

 

Evaluate the indefinite integral
∫ ((r^2)/(r+6))dr
_____________+C

 

((r^2)/2)-6r+(6^2)ln(abs(r+6))
The work

Point Cost: 3

3.

 

 

Evaluate the indefinite integral
∫ (2/(x^2-25))dx
_________+C

 

(2/(2*5))ln(abs((x-5)/(x+5)))
The work

Point Cost: 3

4.

 

 

Evaluate the integral
a= 4
b=3
∫ ((9x+11)/(x^2+3x-4))dx

 

2.289517396
The work

Point Cost: 3

5.

 

 

Evaluate the indefinite integral.
∫ ((x^3+13)/(x^2+4x+3))dx
_____________+C

 

(x^2)/2 -4*x + 6*ln(abs(x+1))+7*ln(abs(x+3))
The work

Point Cost: 3

6.

 

Consider the indefinite integral


Then the integrand has partial fractions decomposition

where

a=______

b=______

c=______

integrating term by term, we obtain that

 

a= 25

b= -24

c= 36

∫ = 25ln(abs(x-5))-24ln(abs(x-6))-(36/(x-6))

The work

Point Cost: 3

7.

 

Consider the indefinite integral


Then the integrand has partial fractions decomposition

where

a=______

b=______

c=______

d=______

integrating term by term, we obtain that

 

a= 4

b= 3

c= 5

d= 3

-4/x+3*ln(|x|)+(5/2)*ln(xˆ2+9)+(3/3)*arctan(x/3)

The work

Point Cost: 3

8.

 

Evaluate the integral.   
∫ ((1)/((x+9)(x^2+4)))dx
0.0671077398209968
The work

Point Cost: 3

9.

 

 

Evaluate the integral

∫ ((5x-10)/(x^2-6x+34))dx

 

(5/2)*ln(x*x+-6*x+34)+(5/5)*arctan((x+-3)/5)+C 
The work

Point Cost: 4

10.

 

 

Make a substitution to express the integrand as a rational
dunction and then evaluate the integral
∫ ((cosx)/(5sin^2x+6sinx))dx

 

-ln(abs(5*sin(x)+6))/6 + ln(abs(sin(x)))/6+c     
The work

Point Cost: 3

11.

 

Evaluate the integral
see the work
The work

Point Cost: 4