Randolph College
Department of Mathematics and Computer Science

 

Homework # 7 - Math 1150


The problems on this homework must be done alone.  The honor code is in effect.

You may submit the solutions twice, if you wish.

 First Name:  Last Name:

 

Integrate

1. \( \int \frac{2}{x+3} dx\)

a.  \(\arctan \mid x+3 \mid + c\)

b.  \(\frac{1}{2} \ln (x^2 + 6x + 10) - 3\arctan\mid x+3\mid + c\)

c.  \(\ln (x^2 + 6x + 10) - 5\arctan\mid x+3\mid + c\)

d.  \(2\ln\mid x+3\mid + c\)

e.  \(\frac{1}{2}\ln(x^2+6x+10)+c\)

 

2. \( \int \frac{1}{x^2+6x+10} dx\)

a.  \(\arctan \mid x+3 \mid + c\)

b.  \(\frac{1}{2} \ln (x^2 + 6x + 10) - 3\arctan\mid x+3\mid + c\)

c.  \(\ln (x^2 + 6x + 10) - 5\arctan\mid x+3\mid + c\)

d.  \(2\ln\mid x+3\mid + c\)

e.  \(\frac{1}{2}\ln(x^2+6x+10)+c\)

 

3. \( \int \frac{x+3}{x^2+6x+10} dx\)

a.  \(\arctan \mid x+3 \mid + c\)

b.  \(\frac{1}{2} \ln (x^2 + 6x + 10) - 3\arctan\mid x+3\mid + c\)

c.  \(\ln (x^2 + 6x + 10) - 5\arctan\mid x+3\mid + c\)

d.  \(2\ln\mid x+3\mid + c\)

e.  \(\frac{1}{2}\ln(x^2+6x+10)+c\)

 

4. \( \int \frac{x}{x^2+6x+10} dx\). (Hint: \(x = (x+3) - 3\) )

a.  \(\arctan \mid x+3 \mid + c\)

b.  \(\frac{1}{2} \ln (x^2 + 6x + 10) - 3\arctan\mid x+3\mid + c\)

c.  \(\ln (x^2 + 6x + 10) - 5\arctan\mid x+3\mid + c\)

d.  \(2\ln\mid x+3\mid + c\)

e.  \(\frac{1}{2}\ln(x^2+6x+10)+c\)

 

5. \( \int \frac{2x+1}{x^2+6x+10} dx\)

a.  \(\arctan \mid x+3 \mid + c\)

b.  \(\frac{1}{2} \ln (x^2 + 6x + 10) - 3\arctan\mid x+3\mid + c\)

c.  \(\ln (x^2 + 6x + 10) - 5\arctan\mid x+3\mid + c\)

d.  \(2\ln\mid x+3\mid + c\)

e.  \(\frac{1}{2}\ln(x^2+6x+10)+c\)