• A. $\frac{2}{3}{\left(c^x\right)}^{\frac{3}{2}}+C$
• B. $\frac{1}{2}\sqrt{c^x}+C$
• C. $2c^{\frac{x}{2}}+C$
• D. $-c^{\frac{x}{2}}+C$

Answer: Option C

Explanation:

• A. $1 + 2e^{2x}$
• B. $1 + e^{2x}$
• C. $1 +\frac{1}{2} e^{2x}$
• D. $x^2 + e^{2x}$

Answer: Option A

Explanation:

• A. $\sin \left(x{e}^x\right) + C$
• B. $\cos \left(x{e}^x\right) + C$
• C. $\tan \left(x{e}^x\right) + C$
• D. ${\cos }^2 \left(x{e}^x\right) + C$

Answer: Option C

Explanation:

• A. $-2\le x\le 2$
• B. $-2<x<2$
• C. $0\le x\le 2$
• D. $-2\le x\le 0$

Answer: Option B

Explanation:

• A. $\frac{\pi }{3}$
• B. $\frac{3\pi }{4}$
• C. $\frac{2\pi }{3}$
• D. $\frac{\pi }{6}$

Answer: Option C

Explanation:

• A. (-1, 0)
• B. (-c, 0)
• C. (c, -c)
• D. (-c, c)

Answer: Option B

Explanation:

• A. 3
• B. 2
• C. 7
• D. 5

Answer: Option B

Explanation:

• A. $\frac{5^{7x}}{7\text{in5}}+c$
• B. $\frac{5^{7x}}{\text{in5}}+c$
• C. $5^{7x}\ln 5+c$
• D. $5^{7x}\left(7\ln 5\right)+c$

Answer: Option A

Explanation:

• A. $\frac{1}{3}$
• B. $\frac{1}{6}$
• C. $\frac{1}{2}$
• D. $-\frac{1}{6}$

Answer: Option B

Explanation:

• A. ${\sin }^{-1}x+\sqrt{\left(1-x^2\right)}+c$
• B. $x {\sin }^{-1}x+\sqrt{\left(1-x^2\right)}+c$
• C. ${\sin }^{-1}x+c$
• D. ${\sin }^{-1}x+\sqrt{\left(1-x\right)}+c$

Answer: Option B

Explanation:

• A. $2e^{e^{2x}}+c$
• B. $e^{2x+1}+c$
• C. $\frac{1}{2}{e}^{2x}+c$
• D. $\frac{1}{2}{e^e}^{2x}+c$

Answer: Option D

Explanation:

• A. $\frac{1}{2}{e}^{2x}+c$
• B. $e^{2x}+c$
• C. $\frac{1}{2}{e}^x+c$
• D. $2e^{2x}+c$

Answer: Option A

Explanation:

• A. $e^x\sin x+c$
• B. $-e^x\sin x+c$
• C. $e^x\cos x+c$
• D. $-e^x\cos x+c$

Answer: Option A

Explanation:

• A. $e^{x}sec x+C$
• B. $e^x\tan x+C$
• C. $e^{x}sec x \tan x+C$
• D. $e^x sec x+C$

Answer: Option A

Explanation:

• A. $x{\left(Inx\right)}^2+2x\ln x+2x+c$
• B. $x{\left(Inx\right)}^2-2x\ln x+2x+c$
• C. $x{\left(Inx\right)}^2-2x\ln x-2x+c$
• D. $x{\left(Inx\right)}^2-2x\ln x+2x+c$

Answer: Option D

Explanation: