Question

find the integration of x^3+x^2+x-1÷x-1×dx​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

CORRECT QUESTION.

⇒ ∫x³ - x² + x - 1/(x - 1).dx.

EXPLANATION.

⇒ ∫x³ - x² + x - 1/(x - 1).dx

As we know that,

We can write equation as,

⇒ ∫x²(x - 1) + 1(x - 1)/(x - 1).dx.

⇒ ∫(x² + 1)(x - 1)/(x - 1).dx.

⇒ ∫(x² + 1).dx

As we know that,

⇒ ∫xⁿdx = xⁿ⁺¹/n + 1 + c.

Using this formula in equation, we get.

⇒ x³/3 + x + 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.