Question

Ahola Users❤❤❤❤❤❤❤
⭐Question in attachment plz solve⭐
Thanks for help☺
#Be Brainly

Answer 1

$\bold{Answer :}$

Let us take, x - 3 = z² ⇒ x = z² + 3

Then, dx = 2z dz

So, x + 2 = z² + 3 + 2 = z² + 5

⇒ z = (x - 3)^(1/2) ...(i)

Now,

∫ (x + 2) √(x - 3) dx

= ∫ (z² + 5) z (2z dz)

= ∫ (2 z⁴ + 10 z²) dz

= 2 ∫ z⁴ dz + 10 ∫ z² dz

= 2 {z⁴⁺¹ / (4 + 1)} + 10 {z²⁺¹ / (2 + 1)} + c, where c is integral constant

= (2/5) z⁵ + (10/3) z³ + c

= {(2/5) (x - 3)^(5/2)} + {(10/3) (x - 3)^(3/2)} + c, using (i) no. equation

= [2 (x - 3)^(3/2) {1/5 (x - 3) + 5/3] + c

= [2 (x - 3)^(3/2) {3 (x - 3) + (5 × 5)}/15] + c

= 2/15 [(x - 3)^(3/2) (3x - 9 + 25)] + c

= 2/15 [(x - 3)^(3/2) (3x + 16)] + c

#$\bold{MarkAsBrainliest}$

Answer 2

$Answer : \boxed { \frac{2}{15} (3x + 16)(x - 3)^{\frac{3}{2}}+ C}$

Hope it helps!