math

U-Subsitution

100

S x(4x^2+3)^3 dx

1/32 (4x^2+3)^4+c

200

S (x^2)/(1+x^3)^2

-1/3 (1+x^3)^-1 +c

300

S tan^4x sec^2x dx

1/5 tanx^5 +c

400

S sinx/cos^2x dx

2cosx+c

500

s (3x-5)^8 dx

1/27 (3x-5)^9 +c

trig Integrals

100

S sec^2(x)

tan(x) +c

200

S e^x dx

e^x+c

300

S top: pi over 6, bottom: -pi over 6 

Sec^2x dx

1.15

400

S SecxTanx dx

secx+c

500

S  top: pi, bottom: 0

(1+sinx)dx

7.8

implicit differentiation

100

if 5-y^3 = xy, find dy/dx at the point (4,1)

dy/dx=1/-7

200

d^2y/dx^2

4xy^2-4x^4/y^3 = d^2y/dx^2

300

find dy/dx when -y^2+x+x^2=-2y^3

dy/dx= 1+2x/-6y^2+2y

400

find dy/dx given that 2x^3=2y^2-4x^2+x-5

dy/dx= 6x^2 + 8x - 1/4y

500

if 2x^3 - y^3 =10, find d^2y/ dx^2

dy/dx= 2x^2/y^2

chain rule

100

let f(x)=6x+3 and g(x)=-2x+5

find h'(x) where h(x)=f(g(x))

h'(x)=-12

200

let f(x)=e^x, g(x)=4x

h'(x), h(x)=f(g(x))

h'(x)=4e^4x

300

f(x)=e^x, g(x)=3x^2+2

find h'(x) where h(x)=f(g(x))

h'(x)=6xe^3x^2+2

400

given f(x)=(5x-3)^2

f'(x)=2(5x-3)'5(5)

=10(5x-3)

500

y=tan(6x)

=6sec^2(6x)

indefinite integrals

100

S 7(x+3)^2 dx

7/3x^3 + 21x^2 + 63x + c

200

s (7x^5-3x^3-4)/(4x) dx

7/20x^5-1/4x^3-ln|x|+c

300

S 5x^2 Cos(5x^3) dx

1/3 Sin(5x^3) + C

400

S -Sec(x)Tan(x)dx

-Secx+c

500

S 24x (e^4x^2-1) dx

3e^ 4x^2-1