Question

do Integration please
$\huge \blue \int( {x}^{3} - 2 {x}^{2} + c)dx$
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Answer 1

EXPLANATION.

⇒ ∫(x³ - 2x² + c)dx.

As we know that,

We can integrate individually, we get.

⇒ ∫(x³)dx - ∫(2x²)dx + ∫(c)dx.

⇒ x³⁺¹/3 + 1 - 2x²⁺¹/2 + 1 + cx + D.

⇒ x⁴/4 - 2x³/3 + cx + D.

                                                                                                                             

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,

We get answer by individual integration,

$\bf \int(x³)dx - \int (2x²)dx + \int(c)dx$

$\bf \: {x}^{3 + 1} /3 + 1 - 2 {x}^{2 + 1} /2 + 1 + cx + D$

$\bf {x}^{4} /4 - 2x³/3 + cx + D$