Question

Integrate the following with respect to x.

(i) x log x 

(ii) 27 x² e^3x 

(iii) x² cos x 

(iv) x³ sin x

Answer 1

(i) I = ∫x log x dx

(ii) I = ∫27 x² e^3x dx = 27∫x² e^3x dx

Applying Bernoulli's formula

(iii) I = ∫x² cos x dx

Applying Bernoulli's formula

(iv) I = ∫x³ sin x dx

Applying Integration by parts,