TEST 8
1.
\(\displaystyle\int \samefrac{\arctan x}{1+x^2}\,dx=?\)
A) \(\arctan x+c\)B) \(\samefrac{\arctan^2x}2+c\)C) \(\operatorname{arccot}x+c\)D) \(\samefrac{\operatorname{arccot}^2x}2+c\)E) \(\arcsin x+c\)
2.
\(\displaystyle\int (\cos^2x\cdot\sin x)\,dx=?\)
A) \(-\samefrac{\cos^3x}3+c\)B) \(\samefrac{\cos^3x}3+c\)C) \(\samefrac{\sin^3x}3+c\)D) \(-\samefrac{\sin^3x}3+c\)E) \(\samefrac{\sin(2x)}3+c\)
3.
\(\displaystyle\int (\cos^3x\cdot\sin^2x)\,dx=?\)
A) \(\samefrac{\sin^3x}3-\samefrac{\sin^4x}4+c\)B) \(\samefrac{\sin^3x}3-\samefrac{\cos^5x}5+c\)C) \(\samefrac{\sin^3x}3-\samefrac{\sin^5x}5+c\)D) \(\samefrac{\cos^4x}4-\samefrac{\sin^3x}3+c\)E) \(\samefrac{\cos^5x}5-\samefrac{\sin^3x}3+c\)
4.
\(\displaystyle\int \samefrac{e^x}{e^x+3}\,dx=?\)
A) \(\ln|e^x+3|+c\)B) \(\ln\left|\samefrac1{e^x+3}\right|+c\)C) \(x\cdot\ln3+c\)D) \(\ln|e^x|+c\)E) \(-\ln|e^x|+c\)
5.
\(\displaystyle\int \samefrac{\sin(2x)}{1+\sin^2x}\,dx=?\)
A) \(\ln|\sin^2x|+c\)B) \(x+\ln|\sin^2x|+c\)C) \(\ln|\sin(2x)|+c\)D) \(\ln|1+\sin^2x|+c\)E) \(\ln|1+\sin x|+c\)
6.
\(\displaystyle\int \cos^2x\,dx=?\)
A) \(\samefrac{\cos^3x}3+c\)B) \(\samefrac{\sin^3x}3+c\)C) \(\samefrac{\sin(2x)}2+x+c\)D) \(\samefrac{\sin(2x)}4+\samefrac x2+c\)E) \(\samefrac{\cos(2x)}4+\samefrac x2+c\)
7.
\(\displaystyle\int\samefrac{dx}{1+9x^2}=?\)
A) \(\arctan(3x)+c\)B) \(3\arctan(3x)+c\)C) \(\samefrac{1}{3}\arctan(3x)+c\)D) \(\samefrac{1}{9}\arctan(9x)+c\)E) \(\samefrac{1}{9}\arctan(3x)+c\)
8.
\(\displaystyle\int\samefrac{dx}{\sqrt{1-4x^2}}=?\)
A) \(\samefrac{1}{2}\arccos(2x)+c\)B) \(\arccos(2x)+c\)C) \(2\arcsin(2x)+c\)D) \(\arcsin(2x)+c\)E) \(\samefrac{1}{2}\arcsin(2x)+c\)