TEST 13
1.
\(\displaystyle\int \samefrac1{\cos^2(5x)}\,dx=?\)
A) \(\tan(5x)+c\)B) \(\cot(5x)+c\)C) \(\samefrac{\tan(5x)}5+c\)D) \(\samefrac{\cot(5x)}5+c\)E) \(-\samefrac{\tan(5x)}5+c\)
2.
\(\displaystyle\int (P(x)\cdot P'(x))\,dx=?\)
A) \(P(x)+c\)B) \(\samefrac{P^2(x)}2+c\)C) \(\samefrac{P(x)}{P\prime(x)}+c\)D) \(P\prime(x)+c\)E) \(\samefrac{[P\prime(x)]^2}2+c\)
3.
\(\displaystyle\int \samefrac{3^{\sqrt x}}{2\sqrt x}\,dx=?\)
A) \(3^{\sqrt x}+c\)B) \(3^{\sqrt x}\cdot\ln3+c\)C) \(\samefrac{3^{\sqrt x}}{\ln\sqrt x}+c\)D) \(\samefrac{3^{\sqrt x}}{\ln3}+c\)E) \(3^{\sqrt x}\cdot\log3+c\)
4.
\(\displaystyle\int\samefrac{e^x dx}{1+e^{2x}}=?\)
A) \(\ln|e^{2x}+1|+c\)B) \(\arctan(e^x)+c\)C) \(2x+c\)D) \(\samefrac{\arctan(e^x)}2+c\)E) \(\operatorname{arccot}(e^x)+c\)
5.
\(\displaystyle\int(\tan^3x\cdot\sec^2x\,dx)=?\)
A) \(\samefrac{\cos^{-4}x}4+c\)B) \(\samefrac{\sin^{-4}x}4+c\)C) \(\samefrac{\cot^4x}4+c\)D) \(\samefrac{\tan^4x}4+c\)E) \(\samefrac{\cot^2x}2+c\)
6.
\(\displaystyle\int \samefrac1{x^2+6x+10}\,dx=?\)
A) \(\operatorname{arccot}(x+3)+c\)B) \(-\samefrac1{(x+3)}+c\)C) \(\samefrac1{x+3}+c\)D) \(\arctan(x+3)+c\)E) \(\arctan(x+3)^2+c\)
7.
\(\displaystyle\int x(x+1)^3\,dx=?\)
A) \(\samefrac{(x+1)^5}5-\samefrac{(x+1)^4}4+c\)B) \(\samefrac{(x+1)^5}5-\samefrac{(x+1)^3}3+c\)C) \(\samefrac{x^5}{5}-\samefrac{x^3}{3}+c\)D) \(\samefrac{(x+1)^5}5+\samefrac{(x+1)^3}3+c\)E) \(\samefrac{x^5}{5}+\samefrac{x^3}{3}+c\)
8.
\(\displaystyle\int \samefrac{1+\cos(2x)}{\sin(2x)}\,dx=?\)
A) \(\ln|\sin(2x)|+c\)B) \(-\ln|\cos(2x)|+c\)C) \(\cot x+c\)D) \(\ln|\cos x|+c\)E) \(\ln|\sin x|+c\)