Bài tập Nguyên hàm của hàm số lượng giác lớp 12 (có lời giải)

A. \(\int {f\left( x \right)dx} = x - \cos x + C\);

B. \(\int {f\left( x \right)dx} = x + \sin x + C\);

C. \(\int {f\left( x \right)dx} = x + \cos x + C\);

D. \(\int {f\left( x \right)dx} = \cos x + C\).

A. \(\int {f\left( x \right)dx} = x + \tan x + C\);

B. \(\int {f\left( x \right)dx} = x + \cot x + C\);

C. \(\int {f\left( x \right)dx} = x - \tan x + C\);

D. \(\int {f\left( x \right)dx} = x - \cot x + C\).

A. sinx + 3x² + C;

B. −sinx + 3x² + C;

C. sinx + 6x² + C;

D. −sinx + C.

A. \(\int {\left( {2\sin x + 3x} \right)dx} = - 2\cos x + \frac{3}{2}{x^2} + C\);

B. \(\int {\left( {2\sin x + 3x} \right)dx} = 2\cos x + 3{x^2} + C\);

C. \(\int {\left( {2\sin x + 3x} \right)dx} = {\sin ^2}x + \frac{3}{2}x + C\);

D. \(\int {\left( {2\sin x + 3x} \right)dx} = \sin 2x + \frac{3}{2}{x^2} + C\).

A. lnx – cosx + C;

B. \( - \frac{1}{{{x^2}}} - \cos x + C\);

C. ln|x| + cosx + C;

D. ln|x| − cosx + C.

A. \(\int {\cos \frac{x}{2}\sin \frac{x}{2}dx} = \frac{1}{2}\sin x + C\);

B. \(\int {\cos \frac{x}{2}\sin \frac{x}{2}dx} = \frac{1}{2}\cos x + C\);

C. \(\int {\cos \frac{x}{2}\sin \frac{x}{2}dx} = - \frac{1}{2}\sin x + C\);

D. \(\int {\cos \frac{x}{2}\sin \frac{x}{2}dx} = - \frac{1}{2}\cos x + C\).

A. \(\int {f\left( x \right)dx} = 3\sin x - 2\ln \left| x \right| - 4\cot x + C\);

B. \(\int {f\left( x \right)dx} = 3\sin x - 2\ln x - 4\cot x + C\);

C. \(\int {f\left( x \right)dx} = 3\sin x - 2\ln x + 4\cot x + C\);

D. \(\int {f\left( x \right)dx} = - 3\sin x - 2\ln x - 4\cot x + C\).

A. F(x) = sinx + cosx + C;

B. F(x) = sinx – cosx + C;

C. F(x) = −sinx + cosx + C;

D. F(x) = −sinx – cosx + C.

A. \(\int {f\left( x \right)dx} = \frac{{4{{\sin }^3}x}}{3} + C\);

B. \(\int {f\left( x \right)dx} = 2x - \sin 2x + C\);

C. \(\int {f\left( x \right)dx} = \frac{{\cos 2x}}{2} + C\);

D. \(\int {f\left( x \right)dx} = 2x - 2\sin 2x + C\).

A. \(\int {f\left( x \right)dx} = 2\sin \left[ {2\left( {x + \pi } \right)} \right] - {x^3} + C\);

B. \(\int {f\left( x \right)dx} = \sin 2x - {x^3} + C\);

C. \(\int {f\left( x \right)dx} = - \sin \left[ {2\left( {x + \pi } \right)} \right] - {x^3} + C\);

D. \(\int {f\left( x \right)dx} = - 4\sin \left[ {2\left( {x + \pi } \right)} \right] - 6x + C\).