Integrate the following functions- -x-9-4 x2 d x

∫x/9 4x^2dx Let 9 4x^2=t ⇒ 8x =dt/dx⇒ dx =dt/ 8x ∴∫x/9 4x^2dx =∫x/tdt/ 8x=1/ 8∫1/tdt =1/ 8log |t|+C = 1/8log |9 4x^2|+C =1/8log | 1/9 4x^2 |+C [ ∴ a log b ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Functions

Integrate the...

Question

Integrate the following functions.
$\int \frac{x}{9 - 4 x^{2}} d x .$

Open in App

Solution

$\int \frac{x}{9 - 4 x^{2}} d x$
Let $9 - 4 x^{2} = t \Rightarrow - 8 x = \frac{d t}{d x} \Rightarrow d x = \frac{d t}{- 8 x}$
$∴ \int \frac{x}{9 - 4 x^{2}} d x = \int \frac{x}{t} \frac{d t}{- 8 x} = \frac{1}{- 8} \int \frac{1}{t} d t = \frac{1}{- 8} l o g | t | + C = - \frac{1}{8} l o g | 9 - 4 x^{2} | + C = \frac{1}{8} l o g ∣ ∣ \frac{1}{9 - 4 x^{2}} ∣ ∣ + C [∴ - a l o g b = a l o g b^{- 1} = a l o g \frac{1}{b}]$

Suggest Corrections

Similar questions

Integrate the function.
$\int \sqrt{1 - 4 x^{2}} d x .$

Integrate the following functions.
$\int \frac{1}{\sqrt{9 - 25 x^{2}}} d x$

Q. Evaluate

\int \frac{x}{9 - 4 x^{2}} d x

Q. Solve

\int \frac{x}{9 - 4 x^{2}} d x

Integrate the following functions.
$\int \frac{1}{9 x^{2} + 6 x + 5} d x .$

Join BYJU'S Learning Program

Integrate the following functions. ∫x9−4x2dx.

∫x9−4x2dx Let 9−4x2=t⇒−8x=dtdx⇒dx=dt−8x ∴∫x9−4x2dx=∫xtdt−8x=1−8∫1tdt=1−8log|t|+C=−18log|9−4x2|+C=18log∣∣19−4x2∣∣+C[∴−a logb=a logb−1=a log1b]

Integrate the following functions.
$\int \frac{x}{9 - 4 x^{2}} d x .$