Math 52

U got this

What should be f(x) and g’(x)?

derive ln(x)

1/x

derive e^(2x)

2e^(2x)

Integration by parts (IBP)

integrate e^cosx

Not integratable

∫1/x

ln(lxl)

∫1/(ax+b)

u = ax+b

∫x/(x²+a²)

u= x²+a²

Algebraic Manipulation

Rewrite the numerator: u² = -(-u²) = -(1 - u² - 1)

2. Distribute negative

3. cancels out the numerator

power-reduction identity

Power reduction identity

trig sub

trig sub

trig sub

trig sub

-cotx

Sec²x-1

Tan²x

sin2x

2sinxcosx

INTEGRATE