1
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{3 x+4}{x^3-2 x+4} d x=\log f(x)+C \Rightarrow f(3)=$$

A
$$\frac{1}{\sqrt{17}}$$
B
$$\frac{1}{17}$$
C
$$\frac{2}{15}$$
D
$$\frac{2}{17}$$
2
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{e^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right] d x=$$

A
$$ e^{\tan ^{-1} x}\left(\tan ^{-1} x\right)^2+C $$
B
$$ e^{\tan ^{-1} x}\left(\sec ^{-1} x\right)^2+C $$
C
$$ e^{\tan ^{-1} x}\left(\sec ^{-1}\left(\sqrt{1+x^2}\right)\right)+C $$
D
$$ e^{\tan ^{-1}} \times\left(\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right)+C $$
3
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{d x}{(x-3)^{\frac{4}{5}}(x+1)^{\frac{6}{5}}}=$$

A
$$\frac{5}{4} \sqrt[5]{\frac{x-3}{x+1}}+C$$
B
$$\frac{5}{4}\left(\frac{x+1}{x-3}\right)^{\frac{1}{5}}+C$$
C
$$\frac{1}{5}\left(\frac{x-3}{x+1}\right)^{\frac{1}{5}}+c$$
D
$$\frac{5}{4}\left(\frac{x-3}{x+4}\right)^{\frac{4}{5}}+C$$
4
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$I_n=\int\left(\cos ^n x+\sin ^n x\right) d x$$ and $$I_n-\frac{n-1}{n} I_{n-2} =\frac{\sin x \cos x}{n} f(x)$$, then $$f(x)=$$

A
$$\cos ^{n-2} x+\sin ^{n-2} x$$
B
$$\cos ^{n-2} x-\sin ^{n-2} x$$
C
$$\frac{\cos ^{n-2} x-\sin ^{n-2} x}{n}$$
D
$$\frac{\cos ^{n-2} x+\sin ^{n-2} x}{n}$$
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