TEST 22
1.
\(A=\displaystyle\int \samefrac{\sqrt{2+\sqrt x}}{\sqrt x}\,dx\)
\(u=2+\sqrt x\)
\(\Rightarrow A=?\)
A) \(\displaystyle\int \samefrac{\sqrt u}2\,du\)B) \(\displaystyle\int \samefrac{2\sqrt u}u\,du\)C) \(\displaystyle\int \samefrac{\sqrt u}{2u}\,du\)D) \(\displaystyle\int 2\sqrt u\,du\)E) \(\displaystyle\int \samefrac{\sqrt u}u\,du\)
2.
\(\displaystyle\int (\tan^3x+\tan x)\,dx=?\)
A) \(\samefrac{\tan^2x}2+c\)B) \(\samefrac{\tan^4x}4+\samefrac{\tan^2x}2+c\)C) \(\samefrac{\cot^2x}2+c\)D) \(\samefrac{\sin^3x}3+\cos x+c\)E) \(\samefrac{\cos^3x}3+\sin x+c\)
3.
\(\displaystyle\int (f(3x-1)\cdot f'(3x-1))\,dx=?\)
A) \(\samefrac{f^2(3x-1)}2+c\)B) \(\samefrac{f^2(3x-1)}6+c\)C) \(\samefrac{3f^2(3x-1)}2+c\)D) \(\samefrac{2f^2(3x-1)}3+c\)E) \(f^2(3x-1)+c\)
4.
\(\displaystyle\int \samefrac{3x^3+2x}{x^2}\,dx=?\)
A) \(3x+\samefrac2x+c\)B) \(3x^2+2x+c\)C) \(\samefrac{3x^2}2+\ln|x|+c\)D) \(x^2+2\cdot\ln|x|+c\)E) \(\samefrac{3x^2}2+2\ln|x|+c\)
5.
\(\displaystyle\int \samefrac{3x+5}{2x+1}\,dx=?\)
A) \(x+\samefrac{7}{2}\ln|2x+1|+c\)B) \(\samefrac{3}{2}+\samefrac{7}{2}\ln|2x+1|+c\)C) \(\samefrac{3x}2+\samefrac{7}{4}\ln|2x+1|+c\)D) \(\samefrac{3x}2+\samefrac{7}{2}\ln|x|+c\)E) \(\samefrac{3x}2+\samefrac{7}{2}\ln|2x+1|+c\)
6.
\(\displaystyle\int \samefrac{x+1}{x^2+5x+6}\,dx=?\)
A) \(\ln\samefrac{(x+3)^2}{|x+2|}+c\)B) \(\ln\left|\samefrac{x+3}{x+2}\right|+c\)C) \(\ln\samefrac{|x+3|}{(x+2)^2}+c\)D) \(\ln\samefrac{\sqrt{x+3}}{|x+2|}+c\)E) \(\ln\samefrac{|x+3|}{\sqrt{x+2}}+c\)
7.
\(\displaystyle\int (x-2)\cdot e^x\,dx=?\)
A) \(x\cdot e^x-e^x+c\)B) \(x\cdot e^x-2e^x+c\)C) \(x\cdot e^x+e^x+c\)D) \(x\cdot e^x-3e^x+c\)E) \(x\cdot e^x+3e^x+c\)
8.
\(\displaystyle\int (x\cdot\cos x)\,dx=?\)
A) \(x\cdot\sin x+\cos x+c\)B) \(-x\cdot\sin x+\cos x+c\)C) \(x\cdot\sin x-\cos x+c\)D) \(x\cdot\sin x+\sin x+c\)E) \(-x\cdot\sin x-\cos x+c\)