Question

what is the integral of (x³-5x²+7x-11)dx​

Answer 1

EXPLANATION.

⇒ ∫(x³ - 5x² + 7x - 11)dx.

As we know that,

In this type of integration we integrate individually, we get.

⇒ ∫(x³)dx - ∫(5x²)dx + ∫(7x)dx - ∫(11)dx.

⇒ x³⁺¹/3 + 1 - 5x²⁺¹/2 + 1 + 7x²/2 - 11x + C.

⇒ x⁴/4 - 5x³/3 + 7x²/2 - 11x + C.

                                                                                                                           

MORE INFORMATION.

Standard integrals.

(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

Now to find the integral,

Use individual integration,

$\bf →\int(x³)dx - \int(5x²)dx + \int(7x)dx - \int(11)dx$

$\bf \: →{x}^{3 + 1} /3+1-5 {x}^{2 + 1} /2+1+7x²/2 - 11x + C$

$\bf \:→ {x}^{4} /4 - 5x³/3 + 7x²/2 - 11x + C$