MA17204 Test 2 Review

Integrals

100

5sinh(7x-2)dx

5/7 cosh(7x+2)+C

200

4ln(x)/x^6 dx

(-5ln(x)-1)/25 +C

300

tan(x)sec^3(x)dx

1/4 sec^4(x) +C

400

5sin^-1(x)dx

5xsin^1(x)-10(1-x^2)^1/2 +C

500

Integral from 2 to infinity of 9/(1-3x)^4

1/125

Derivatives

100

2x^3

6x^2

200

sin(4x)

4cos(4x)

300

log_3(2x+4)

2/(ln3(2x+4))

400

x^4tanh(3x)

4x^3tanh(3x)+3x^4sech^2(3x)

500

ln(cosh(2x))

2tanh(2x)

Dif EQ

100

dy/dx=2xy

ln|y|=x^2+C

200

dy/dx=(x^2-2)(2y+3)

ln|2y+3|=2/3 x^3-4x+C

300

dy/dx=3y^4(x^1/2)

-1/3 y^-3=2x^3/2 +C

400

dy/dx=9+3x+3y+xy

ln|y+3|=1/2 x^2 +3x+C

500

dy/dx=(3x+1)(y^2+4)=3xy^2+12x+y^2+4

(In terms of theta and x

1/8 theta+1/4 sin(2theta)=3/2 x^2 + x +C

Partial Frac Decomp

100

Solve for fractions with new numerators.

(3x+5)

--------

(x+1)(x-2)

-2/3     +       11/3

-------          ---------

x+1                x-2

200

Solve for fractions with new numerators.

x

---------

(x-1)^2

1         +       1

-----         ----------

x-1             (x-1)^2

300

2x+3

------------------

(x^2+1)(x-2)

-7/5 x - 4/5      +     7/5

---------------        ---------

x^2+1                   x-2

400

3x^2+x+2

--------------

(x-1)^2(x+2)

5/3  +      2     +      4/3

-----     ------         --------

x-1        (x-1)^2      x+2

500

x^3+2x^2+x+4

-------------------

(x^2+1)(x-1)^2

  x       +       4  

-------      ---------

x^2+1       (x-1)^2