For each of the following integrals, indicate whether integration by substitution or integration by parts is more appropriate, or if neither method is appropriate. do not evaluate the integrals.

a. ∫ xsinx dx
i. substitution
ii. neither
iii. integration

b. ∫ x⁴/(1+x³). dx
i. substitution
ii. neither
iii. integration

c. ∫ x⁴. e^x³. dx
i. substitution
ii. neither
iii. integration

d. ∫x⁴ cos(x⁵). dx
i. substitution
ii. neither
iii. integration

e. ∫1/√9x+1 .dx
i. substitution
ii. neither
iii. integration

a. ∫ xSinx dx

iii. integration by parts

u =x and dv= sinx

b. ∫ x⁴/(1+x³). dx  

ii. neither

Long division is an option here before integration is done

c. ∫ x⁴. e^x³. dx

i. substitution

where u = x⁵

d. ∫x⁴ cos(x⁵). dx

i. substitution

where u = x⁵

e. ∫1/√9x+1 .dx

i. substitution

where u = 9x+1

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

according to this law, when unemployment goes up by 1%, gdp drops by 2%. in the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the gdp drops by 6%. thus the effect is a drop in gdp by 6%.

step-by-step explanation: