A. \(\int {f(x)dx} = \ln x - \ln {x^2} + C\)
B. \(\int {f(x)dx} = \ln x - \frac{1}{x} + C\)
C. \(\int {f(x)dx} = \ln \left| x \right| + \frac{1}{x} + C\)
D. \(\int {f(x)dx} = \ln \left| x \right| - \frac{1}{x} + C\)
A. \(f(x) = {x^2} + x + 3\)
B. \(f(x) = {x^2} + x - 3\)
C. \(f(x) = {x^2} + x\)
D. \(f(x) = {x^2} -x\)
A. \(\int {f(x) = 2x{e^x} + C}\)
B. \(\int {f(x) = (2x - 1){e^x} + C}\)
C. \(\int {f(x) = (2x - 2){e^x} + C}\)
D. \(\int {f(x) = (2x - 3){e^x} + C}\)
A. \(F(x) = {e^{3x}}\)
B. \(F(x) = - \frac{1}{3}{e^{3x}} + \frac{4}{3}\)
C. \(F(x) = \frac{1}{3}{e^{3x}} + \frac{2}{3}\)
D. \(F(x) = \frac{1}{3}{e^{3x + 1}}\)
A. \(\int {f\left( x \right)d{\rm{x}}} = \frac{2}{5}{x^2}\sqrt x + C\)
B. \(\int {f\left( x \right)d{\rm{x}}} = \frac{1}{5}{x^2}\sqrt x + C\)
C. \(\int {f\left( x \right)d{\rm{x}}} = \frac{2}{5}x\sqrt x + C\)
D. \(\int {f\left( x \right)d{\rm{x}}} = \frac{3}{2}\sqrt x + C\)
A. \(\int {f(x)dx} = - \ln \left| {\cos x} \right| + C\)
B. \(\int {f(x)dx} = \ln \left| {\cos x} \right| + C\)
C. \(\int {f(x)dx} = - \ln \left| {\sin x} \right| + C\)
D. \(\int {f(x)dx} = \ln \left| {\sin x} \right| + C\)
A. \(F\left( 1 \right) = 3 - \ln \frac{7}{3}\)
B. \(F\left( 1 \right) = 3 + \ln \frac{7}{3}\)
C. \(F\left( 1 \right) = 3 - \ln 2\)
D. \(F\left( 1 \right) = 3 + \ln 2\)
A. \(\int {f(x)dx = 2{e^x}(x - 1) - {x^2}}\)
B. \(\int {f(x)dx = 2{e^x}(x - 1) -4 {x^2}}\)
C. \(\int {f(x)dx = 2{e^x}(x - 1) -2 {x^2}}\)
D. \(\int {f(x)dx = 2{e^x}(1-x) - {x^2}}\)
A. \(\int {f(x)dx = x\sqrt {2 - {x^2}} } + C\)
B. \(\int {f(x)dx = - \frac{1}{3}({x^2} + 4)\sqrt {2 - {x^2}} } \) \(+ C\)
C. \(\int {f(x)dx = - \frac{1}{3}{x^2}\sqrt {2 - {x^2}} } + C\)
D. \(\int {f(x)dx = } - \frac{1}{3}({x^2} - 4)\sqrt {2 - {x^2}} \) \(+ C\)
A. \(y = \frac{{{x^4}}}{4} - \frac{{{x^2}}}{2} + 3\)
B. \(y = \frac{{{x^4}}}{4} - \frac{{{x^2}}}{2} - 3\)
C. \(y = \frac{{{x^4}}}{4} + \frac{{{x^2}}}{2} + 3\)
D. \(y = 3{x^2} - 1\)
A. \(I = \frac{1}{{{e^x} + 1}} + C\)
B. \(I = - \frac{1}{{{{\left( {{e^x} + 1} \right)}^2}}} + C\)
C. \(I = {e^{ - x + 1}} + C\)
D. \(I = \frac{{{e^x}}}{{{e^x} + 1}} + C\)
A. \(I = \left( {3{x^2} - 7x + 8} \right){e^x} + C\)
B. \(I = \left( {3{x^2} - 7x} \right){e^x} + C\)
C. \(I = \left( {3{x^2} - 7x + 8} \right) + {e^x} + C\)
D. \(I = \left( {3{x^2} - 7x + 3} \right){e^x} + C\)
A. \( - \frac{1}{4}{\rm{cos}}2x + C\)
B. \(\frac{1}{2}{\sin ^2}x + C\)
C. \( - \frac{1}{2}{\rm{co}}{{\rm{s}}^2}x + C\)
D. \(\frac{1}{2}{\rm{cos}}2x + C\)
A. \(I = x\tan x + \frac{1}{{{\rm{co}}{{\rm{s}}^2}x}} + \frac{2}{{{\rm{cos}}x}} + C\)
B. \(I = x\tan x + \ln \left| {\cos x} \right| + \frac{2}{{{\rm{cos}}x}} + C\)
C. \(I = x\tan x + \ln \left| {\cos x} \right| - \frac{2}{{{\rm{cos}}x}} + C\)
D. \(I = x\tan x - \frac{1}{{{\rm{co}}{{\rm{s}}^2}x}} - \frac{2}{{{\rm{cos}}x}} + C\)
A. 10 m/s
B. 11 m/s
C. 12 m/s
D. 13 m/s
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