Answer:
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
Answer:
Step-by-step explanation:
x - 1/2 =0
2x = 1
4x = 2
Answer:
19
Step-by-step explanation:
2d+3 d=8
2(8)+3
16+3
19
Answer:
Step-by-step explanation:
Let's begin by identifying the lengths of the three sides of the triangle:
length of side 1 = 17
length of side 2 = 2x - 1 (1 less than twice side 3)
length of side 3 = x
Now let's apply the Triangle Inequality Theorem to this triangle:
side 1 + side 2 > side 3:
17 + 2x - 1 > x
16 + 2x > x
2x - x > -16
x > -16 (reject negative measurement)
2x - 1 > -33 (reject negative measurement)
side 1 + side 3 > side 2
17 + x > 2x - 1
x - 2x > -1 - 17
-x > -18
x < 18
2x - 1 < 35
side 2 + side 3 > side 1
2x - 1 + x > 17
3x - 1 > 17
3x > 18
x > 6
2x - 1 > 11
Thus, we have our answers based on the value of x:
6 < x (length of side 3) < 18
11 < 2x - 1 (length of side 2) < 35
Thanks for submitting this problem and glad to help.