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