What is the integral from 3/2 to 6 of x/(sqrt(2x-3)) ?

The integral from 3/2 to 6 of x/(sqrt(2x-3)) is 9

Popular >

integral from 3/2 to 6 of x/(sqrt(2x-3))

\int_{\frac{3}{2}}^{6} \frac{x}{2 x - 3} d x

9

Solution steps

\int_{\frac{3}{2}}^{6} \frac{x}{2 x - 3} d x

Apply u-substitution

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

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

Take the constant out:

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

= \frac{1}{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

= \frac{1}{2} (\int_{0}^{3} u^{2} d u + \int_{0}^{3} 3 d u)

\int_{0}^{3} u^{2} d u = 9

\int_{0}^{3} 3 d u = 9

= \frac{1}{2} (9 + 9)

Simplify

\frac{1}{2} (9 + 9) : 9

= 9

\int_{0}^{2} (9 - x) x d x

\int_{1}^{5} (\frac{x}{2 x - 1}) d x

\int_{- \frac{1}{2}}^{0} (2 x + 1)^{2020} d x

\int_{1}^{8} \frac{2}{t} d t

\int_{0}^{3} f (3 x) d x

What is the integral from 3/2 to 6 of x/(sqrt(2x-3)) ?
The integral from 3/2 to 6 of x/(sqrt(2x-3)) is 9