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1
KCET 2026
MCQ (Single Correct Answer)
+1
-0
$\int e^{-x \log 2} \cdot 2^x\,dx = $
A
$\log x + C$
B
$x + C$
C
$\dfrac{1}{x} + C$
D
$\dfrac{x^2}{2} + C$
2
KCET 2026
MCQ (Single Correct Answer)
+1
-0
If '$n$' is a natural number, then $\int \dfrac{\sin^n x}{\cos^{n+2} x}\,dx = $
A
$\dfrac{\tan^{n-1} x}{n - 1} + C$
B
$\dfrac{\tan^n x}{n} + C$
C
$\dfrac{\tan^{n+2} x}{n + 2} + C$
D
$\dfrac{\tan^{n+1} x}{n + 1} + C$
3
KCET 2025
MCQ (Single Correct Answer)
+1
-0
The value of $\int \frac{\mathrm{dx}}{(\mathrm{x}+1)(\mathrm{x}+2)}$ is
A
$\log \left|\frac{\mathrm{x}-1}{\mathrm{x}+2}\right|+\mathrm{c}$
B
$\log \left|\frac{x-1}{x-2}\right|+c$
C
$\log \left|\frac{x+2}{x+1}\right|+c$
D
$\log \left|\frac{x+1}{x+2}\right|+c$
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0
$\int \frac{\mathrm{dx}}{\mathrm{x}^2\left(\mathrm{x}^4+1\right)^{3 / 4}}$ equals
A
$\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+c$
B
$\left(x^4+1\right)^{\frac{1}{4}}+c$
C
$-\left(\mathrm{x}^4+1\right)^{\frac{1}{4}}+\mathrm{c}$
D
$-\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+c$
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