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

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.