How do you integrate ? you!

⅔ √(x + 1) (x − 2) + C

Step-by-step explanation:

∫ x / √(x + 1) dx

Add and subtract 1 to the numerator.

∫ (x + 1 − 1) / √(x + 1) dx

Split the fraction.

∫ [ (x + 1) / √(x + 1) − 1 / √(x + 1) ] dx

∫ [ √(x + 1) − 1 / √(x + 1) ] dx

Rewrite with exponents.

∫ [ (x + 1)^½ − (x + 1)^-½ ] dx

Use u-substitution.

u = x + 1, du = dx

∫ (u^½ − u^-½) du

Integrate using power rule.

⅔ u^(3/2) − 2 u^½ + C

Factor.

u^½ (⅔ u − 2) + C

⅓ u^½ (2 u − 6) + C

Substitute back.

⅓ (x + 1)^½ (2 (x + 1) − 6) + C

Simplify.

⅓ √(x + 1) (2x + 2 − 6) + C

⅓ √(x + 1) (2x − 4) + C

⅔ √(x + 1) (x − 2) + C

the circle one

5104.38 inches

step-by-step explanation: