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Popular >

integral from 3 to 6 of x/(sqrt(x-3))

Solution

\int_{3}^{6} \frac{x}{x - 3} d x

Solution

83

+1

Solution steps

\int_{3}^{6} \frac{x}{x - 3} d x

Apply u-substitution

: \int_{0}^{3} 2 (u^{2} + 3) d u

= \int_{0}^{3} 2 (u^{2} + 3) d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{3} u^{2} + 3 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int_{0}^{3} u^{2} d u + \int_{0}^{3} 3 d u)

\int_{0}^{3} u^{2} d u = 3

\int_{0}^{3} 3 d u = 33

= 2 (3 + 33)

Simplify

= 83

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y = x^{2} - 2, y = 2

implicit 2x^2+y^2=9 implicit derivative

2 x^{2} + y^{2} = 9

Frequently Asked Questions (FAQ)

What is the integral from 3 to 6 of x/(sqrt(x-3)) ?
The integral from 3 to 6 of x/(sqrt(x-3)) is 8sqrt(3)