Question:
\(\displaystyle \int \frac{dx}{25-x^2}=\)
\(\displaystyle \int \frac{dx}{25-x^2}=\)
Show Hint
Remember the standard formula \(\int\frac{dx}{a^2-x^2}=\frac{1}{2a}\log\left|\frac{a+x}{a-x}\right|+c\).
Updated On: May 7, 2026
- \(\frac{1}{5}\log\left|\frac{x-5}{x+5}\right|+c\)
- \(\frac{1}{5}\log\left|\frac{x+5}{x-5}\right|+c\)
- \(\frac{1}{10}\log\left|\frac{5+x}{5-x}\right|+c\)
- \(\frac{1}{10}\log\left|\frac{5-x}{5+x}\right|+c\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
We need to evaluate:
\[
\int \frac{dx}{25-x^2}.
\]
Write
\[
25-x^2=5^2-x^2.
\]
We know the standard formula:
\[
\int \frac{dx}{a^2-x^2}
=
\frac{1}{2a}\log\left|\frac{a+x}{a-x}\right|+c.
\]
Here,
\[
a=5.
\]
Therefore,
\[
\int \frac{dx}{25-x^2}
=
\frac{1}{2(5)}\log\left|\frac{5+x}{5-x}\right|+c.
\]
\[
=
\frac{1}{10}\log\left|\frac{5+x}{5-x}\right|+c.
\]
Hence,
\[
\int \frac{dx}{25-x^2}
=
\frac{1}{10}\log\left|\frac{5+x}{5-x}\right|+c.
\]
Was this answer helpful?
0
0
Top AP ECET Mathematics Questions
- The sum of the four digit even numbers that can be formed with the digits 0,3,5,4 with out repetition is
- A random variable X has the following probability distribution The variance of this random variable is
- For the matrix $A = \begin{pmatrix}3&-3&4\\ 2&-3&4\\ 0&-1&1\end{pmatrix}, A^{-1} = $
- If $A = \begin{bmatrix}k/2&0&0\\ 0&1/3&0\\ 0&0&m/4\end{bmatrix} $ and $A^{-1} = \begin{bmatrix}1/2&0&0\\ 0&1/3&0\\ 0&0&1/4\end{bmatrix}$ then $ k + l + m = $
- Number of ways of forming a committee of $6$ members out of $5$ Indians, $5$ Americans and $5$ Australians such that there will be atleast one member from each country in the committee is
View More Questions
Top AP ECET integral Questions
- If $I_{n} = \int \frac{\sin nx}{\sin x} dx $ for $n = 1, 2 , 3,...,$ then $I_6$ =
- If $I(x)=\int x^{2}(\log x)^{2} d x$ and $I( 1)=0$, then $I(x)$
- The value of \(\displaystyle \int (\log\sec x)\tan x\,dx\) is
- \(\displaystyle \int \sin^2x\,dx=\)
- \(\displaystyle \int_{0}^{\pi/2}\frac{\cos 2x}{\sin x+\cos x}\,dx=\)
View More Questions
Top AP ECET Questions
- The sum of the four digit even numbers that can be formed with the digits 0,3,5,4 with out repetition is
- Thermal decomposition of $HCOOH$ is a first order reaction and the rate constant at T(K) is $4.606 \times 10^{-3}\, s^{-1}$. The time required to decompose $90\%$ of initial quantity of $HCOOH$ at $T(K)$ in seconds is
- Three rods of same dimensions have thermal conductivities 3 K, 2 K and K. They are arranged as shown below:What will be the temperature T of the junction?
- To which group and period does the element belong if the electronic configuration of an element in its $-2$ oxidation state is $1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6}$ ?
- A ball of mass 0.6 kg attached to a light inextensible string rotates in a vertical circle of radius 0.75 m such that it has a speed of $ 5\text{ }m{{s}^{-1}} $ when the string is horizontal. Tension in string when it h horizontal on other side is $ (g=10m{{s}^{-}}2) $
View More Questions