Question

Integrate the following w.r.t.x. :-
(3x - 5)

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Answer 1

Step-by-step explanation:

Integration will be applied separately on

3x and 5

Integrating 3x with respect to x =

$\frac{3 {x}^{2} }{2}$

Integrating 5 with respect to x =

$5x$

So complete integration of 3x - 5 will be

$\frac{3 {x}^{2} }{2} - 5x + c$

Answer 2

EXPLANATION.

⇒ ∫(3x - 5)dx.

As we know that,

We can write equation as,

⇒ ∫(3x)dx - ∫5dx.

As we know that,

Formula of :

⇒ ∫xⁿdx = xⁿ⁺¹/n + 1 + c, (n ≠ -1).

⇒ 3x²/2 - 5x + 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.