Question

How do you integrate
`\int\limits (x)/(√(x+1) ) dx`? Thank you!

Answer 1

yo buzbuz sorry to answer this you can report it if you want can you help me with my spanish? please??

Explanation:

1. Read and choose the option with the correct answer. Soy Faustina y vivo en Miami, Florida, pero soy de Puerto Rico. Cuando era pequeña, los domingos por la mañana, me gustaba mirar a mi abuela cuando tenía la caña de azúcar en su cocina.

Based on the text and what you learned in the lesson, what could Faustina learn from watching her grandmother?

A. How to collect the crop

B. How to cook tembleque

C. How to make clothing

D. How to store the food

2. Read the scenario and choose the option that answers the question.

Lisa era la más joven de la familia.

Based on the text, what is true about Lisa?

A. She was older than the rest.

B. She was younger than the rest.

C. She was the oldest.

D. She was the youngest.

Answer 2

⅔ √(x + 1) (x − 2) + C

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