Question

integrate sqrt(1 + x) dx =​

Answer 1

Answer:

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Answer 2

EXPLANATION.

⇒ ∫√(1 + x) dx.

As we know that,

Using substitution method in this equation, we get.

Let, we assume that.

⇒ 1 + x = t².

Differentiate w.r.t x, we get.

⇒ dx = 2tdt.

Put the values in the equation, we get.

⇒ ∫√(t²) 2tdt.

⇒ ∫t.2tdt.

⇒ ∫2t²dt.

⇒ 2(t³)/3 + c.

Put the value of t = √(1 + x) in the equation, we get.

⇒ 2[√(1 + x)]³/3 + 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.