Evaluating Definite Integrals and Logarithms

Differentiating cos(2x) over 1 + sin(2x)

Integrating cos(2x) over 1 + sin(2x)

Differentiating sin(2x) over 1 + cos(2x)

Integrating sin(2x) over 1 + cos(2x)

Because it is already simplified

Because it involves trigonometric functions

Because the sum is in the numerator

Because the sum is in the denominator

U = 1 + cos(2x)

U = cos(2x)

U = sin(2x)

U = 1 + sin(2x)

Basic trigonometric integral formula

Logarithmic formula

Polynomial formula

Exponential formula

tan(2x) - 1 = sec(2x)

sec(2x) + 1 = tan(2x)

tan(2x) + 1 = sec(2x)

sec(2x) - 1 = tan(2x)

Positive natural log of sqrt(2)/2

Negative natural log of sqrt(2)/2

One

Zero

As a product of two natural logs

As a sum of two natural logs

As a difference of two natural logs

As a single natural log

-1

sqrt(2)/2

1

0

-1

sqrt(2)/2

1

0

log(a/b) = log(a) - log(b)

log(a) = a*log(1)

log(a*b) = log(a) + log(b)

log(a^b) = b*log(a)