evaluate-2x-4x-5-dx-

Question Number 158768 by EbrimaDanjo last updated on 08/Nov/21

evaluate

\int 2 x \sqrt{4 x - 5} dx

Answered by MJS_new last updated on 08/Nov/21

\int 2 x \sqrt{4 x - 5} d x = ?

without substitution :

\frac{d}{d x} [(a x + b) {(4 x - 5)}^{3 / 2}] = (10 a x - 5 a + 6 b) \sqrt{4 x - 5}

\Rightarrow

10 a x - 5 a + 6 b = 2 x

\Rightarrow

a = \frac{1}{5} \land b = \frac{1}{6}

\Rightarrow

\int 2 x \sqrt{4 x - 5} d x = (\frac{x}{5} + \frac{1}{6}) {(4 x - 5)}^{3 / 2} + C

Commented by EbrimaDanjo last updated on 08/Nov/21

thanks sir