Question

integral of ( x²+4) DX explanation plz​

Answer 1

EXPLANATION.

⇒ ∫(x² + 4)dx.

As we know that,

We can write equation as,

⇒ ∫x²dx + ∫4dx.

As we know that,

Formula of :

⇒ ∫xⁿdx = xⁿ⁺¹/n + 1 + c, (n ≠ - 1).

⇒ ∫1.dx = x + c.

Using this formula in the equation, we get.

⇒ x²⁺¹/2 + 1 + 4x + c.

⇒ x³/3 + 4x + c.

                                                                                                                   

MORE INFORMATION.

(1) = ∫0.dx = c.

(2) = ∫1.dx = x + c.

(3) = ∫k dx = kx + c, (k ∈ R).

(4) = ∫xⁿdx = xⁿ⁺¹/n + 1 + c, (n ≠ - 1).

(5) = ∫dx/x = ㏒(x) + c.

(6) = ∫eˣdx = eˣ + c.

(7) = ∫aˣdx = aˣ/㏒a + c = aˣ ㏒e + c.

Answer 2

✪ANSWER GIVEN IN ATTACHMENT WITH EXPLANATION✪