1
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

    If $\int \frac{d x}{\left(x^2+9\right) \sqrt{x^2+16}}=\frac{1}{3 \sqrt{7}} \tan ^{-1}\left(K \frac{x}{\sqrt{16+x^2}}\right)+c$, then $K=$

A

$\frac{\sqrt{7}}{3}$

B

$3 \sqrt{7}$

C

$\frac{3}{\sqrt{7}}$

D

$\frac{3}{7}$

2
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{2 \sin x-3 \cos x}{4 \cos x-3 \sin x} d x= $$

A

$\frac{1}{25}[17 \log |4 \cos x-3 \sin x|-6 x]+C$

B

$\frac{1}{25}[x-18 \log |4 \cos x-3 \sin x|]+C$

C

$\frac{1}{25}[\log |4 \cos x-3 \sin x|-18 x]+C$

D

$\frac{1}{25}[17 x-6 \log |4 \cos x-3 \sin x|]+C$

3
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int e^{4 x}(\sin 3 x-\cos 3 x) d x= $$

A

$\frac{e^{4 x}}{25}(7 \sin 3 x-\cos 3 x)+C$

B

$\frac{e^{4 x}}{25}(\sin 3 x-7 \cos 3 x)+C$

C

$\frac{e^{4 x}}{5}(7 \sin 3 x+\cos 3 x)+C$

D

$\frac{e^{4 x}}{5}(\sin 3 x+7 \cos 3 x)+C$

4
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int\left(\frac{1-\log x}{1+(\log x)^2}\right)^2 d x= $$

A

$\frac{1}{1+(\log x)^2}+C$

B

$\frac{\log x}{1+(\log x)^2}+C$

C

$\frac{x}{1+(\log x)^2}+C$

D

$\frac{x^2}{1+(\log x)^2}+C$

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