M408D Midterm #1

integrals to know

secx

ln| tanx + secx | +c

integral of tanx

-ln |cosx| +c

cosx

sinx

sinx

-cosx

what identity equals sec²x

1 + tan²x

what identity equals csc²x

1 + cot²x

what identity equals 1

cos²x + sin²x

what is cot

1/tanx

what csc

1/sinx

what is sec

1/cosx

half angle identity for sin²x

½(1-cos2x)

half angle identity for cos²x

½(1+cos(2x))

double angle identity for sin(2x)

2sinxcosx

what is cosxsinx

2sin(2x) OR (sin²(x))/2

integral of e^ 2x

e^(2x)/2

integral of sqrt x

2x^(3/2) / 3

integral of cos(pi * x)

sin(pix)/pi

integral of ln(x)

xln(x) -x

derivative of cos^-1

-1/sqrt (1-x²)

integral of any regular fraction (ex: 5/4)

5x/4 (add x to numerator)

integral of csc²x

-cot(x)

integral of csc

-ln | cscx + cot(x) | +c

integral of cotx

ln|sinx|+c

what is sqrt (x²-a²)

asecx

what is sqrt(a²-x²)

asinx

what is sqrt(a²+x²)

atanx

cos(2x)

2cos(x)²-1

tan (x+y)=

tan(x) + tan(y)/1-tan(x)tan(y)

sin (x/2)²

1-cos(x)/2

cos(x/2)²

1+cos(x)/2

sin (x + y)

sin(x)cos(y) + sin(y)cos(x)

cos(x+y)

cos(x)cos(y) + sin(x)sin(y)

cos and sin (pi/2)

(0,1)

cos and sin (pi/4)

(sqrt2/2, sqrt2/2)

cos and sin (pi)

(-1,0)

cos and sin (pi/6)

(sqrt3/2, ½)

cos and sin (3pi/2)

(0,-1)

derivative of tanx

sec²x

derivative of secx

tanxsecx

derivative of cotx

-csc(x)²

derivative of csc

-cotxcscx

derivative of arcsin

1/sqrt(1-x²)

derivative of arctan

1/1+x²