Points Q and R are midpoints of the sides of triangle ABC.

Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx x(l

Pepsi [2]

I'm assuming the integral is

$\displaystyle \int \frac{dx}{x (\ln(x^2))^5}$

We have

$\ln(x^2) = 2 \ln|x| \implies (\ln(x^2))^5 = 32 (\ln|x|)^5$

Then substituting $y=\ln|x|$ and $dy=\frac{dx}x$ , the integral transforms and reduces to

$\displaystyle \int \frac{dx}{x(\ln(x^2))^5} = \frac1{32} \int \frac{dy}{y^5} \\\\ ~~~~~~~~ = \frac1{32} \left(-\frac1{4y^4}\right) + C \\\\ ~~~~~~~~ = -\frac1{128(\ln|x|)^4} + C$

which we can rewrite as

$128 (\ln|x|)^4 = 8\cdot2^4(\ln|x|)^4 = 8 (2\ln|x|)^4 = 8 (\ln(x^2))^4$

and so

$\displaystyle \int \frac{dx}{x (\ln(x^2))^5} = \boxed{-\frac1{8(\ln(x^2))^4} + C}$

7 0

10 months ago

9. A ladder of length 23 feet leans against the side of a building. The angle of elevation of the ladder is 76. Find the distanc

irakobra [83]

<h3>Answer:</h3>

B) 22.32 feet

$\quad\rule{300pt}{1pt}$

<h3>Solution:</h3>

we are given that , a ladder is placed against a side of building , which forms a right angled triangle . We wre given one side of a right angled triangle ( hypotenuse ) as 23 feet and the angle of elevation as 76 ° . We can find the Perpendicular distance from the top of the ladder go to the ground by using the trigonometric identity:

$\qquad\quad\bull ~{\boxed{\bf{ Sin\theta =\dfrac{Perpendicular}{Hypotenuse}}} }~\bull$