Question

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

Answer 1

Answer:

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