Tìm họ nguyên hàm của hàm số fxx 2 + 1

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Câu hỏi:
Tìm nguyên hàm của hàm số f[x] = 2x +1.

A. \[% MathType!MTEF!2!1!+-
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\int {\left[ {2x + 1} \right]} {\rm{d}}x = \frac{{{x^2}}}{2} + x + C\]

B. \[% MathType!MTEF!2!1!+-
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\int {\left[ {2x + 1} \right]} {\rm{d}}x = {x^2} + x + C\]

C. \[% MathType!MTEF!2!1!+-
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\int {\left[ {2x + 1} \right]} {\rm{d}}x = 2{x^2} + 1 + C\]

D. \[% MathType!MTEF!2!1!+-
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\int {\left[ {2x + 1} \right]} {\rm{d}}x = {x^2} + C\]

Lời Giải:
Đây là các câu trắc nghiệm về NGUYÊN HÀM mức độ 1,2

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\int {\left[ {2x + 1} \right]} {\rm{d}}x = {x^2} + x + C\]

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Thuộc chủ đề: Trắc nghiệm Nguyên hàm

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Câu hỏi:
CÂU HỎI:
Họ nguyên hàm của hàm số \[f[x]=x \ln 2 x\] là:

A. \[\begin{aligned}
&\frac{x^{2}}{2}\left[\ln 2 x-\frac{1}{2}\right]+C
\end{aligned}\]

B. \[x^{2} \ln 2 x-\frac{x^{2}}{2}+C \text { . }\]

C. \[\frac{x^{2}}{2}[\ln 2 x-1]+C . \]

D. \[ \frac{x^{2}}{2} \ln 2 x-x^{2}+C .\]

Lời Giải:
Đây là các câu trắc nghiệm về NGUYÊN HÀM mức độ 2,3 – VẬN DỤNG

\[\text { Đặt }\left\{\begin{array} { l }
{ u = \operatorname { l n } 2 x } \\
{ \mathrm { d } v = x \mathrm { d } x }
\end{array} \rightarrow \left\{\begin{array}{l}
\mathrm{d} u=\frac{1}{x} \\
v=\frac{x^{2}}{2}
\end{array} .\right.\right.\]

Khi đó:

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\[\begin{aligned}
&F[x]=\int f[x] \mathrm{d} x=\frac{x^{2}}{2} \cdot \ln 2 x-\int \frac{1}{x} \cdot \frac{x^{2}}{2} \mathrm{~d} x \\
&=\frac{x^{2}}{2} \ln 2 x-\frac{x^{2}}{4}+C=\frac{x^{2}}{2}\left[\ln 2 x-\frac{1}{2}\right]+C
\end{aligned}\]

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Thuộc chủ đề: Trắc nghiệm Nguyên hàm