1
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language
 What is $\int \frac{dx}{10^{x}+10^{-x}}$ equal to?
1
$\tan ^{-1}(10^{x})+c $
2
$(\ln 10)\tan ^{-1}(10^{x})+c $
3
$\frac{1}{\ln 10}\tan ^{-1}(10^{x})+c $
4
$\ln (10^{x}+10^{-x})+c$
2
NDA Mathematics 13 April 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Consider the following for the two (02) items that follow:

Let the function y = (1 - cos x)-1 where$x \ne 2n\pi$ and n is an integer

What is ydx equal to? 

where c is the constant of integration.

A
tan(x/2)+c
B
cot(x/2)+c
C
tan(x/2)+c
D
cot(x/2)+c
3
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Direction : Consider the following for the items that follow :

Let $\rm 2\int\frac{x^2-1}{\sqrt{x^2+1}}dx=U(x) V(x)-3\ln \{U(x)+V(x)\}+c$

What is |U2(x) - V2(x)| equal to?
1
0
2
1
3
2
4
3
4
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Direction : Consider the following for the items that follow :

Let $\rm 2\int\frac{x^2-1}{\sqrt{x^2+1}}dx=U(x) V(x)-3\ln \{U(x)+V(x)\}+c$

What is U(x) V(x) equal to? 
1
$\rm\sqrt{x^2+x^4}$
2
$\rm\sqrt{x+x^3}$
3
$\rm \frac{\sqrt{x^2+x^4}}{2}$
4
$\rm 2\sqrt{x^2+x^4}$