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# ϕ̌g

1. ̕sϕȂD
2.  $3\displaystyle{ \int \( {x}^{3}+2{x}^{2}- \sqrt{x} \) dx }$ $3\displaystyle{ \int \frac{\hspace{2}3\hspace{2}}{\hspace{2} \sqrt{ x+1 }- \sqrt{x} \hspace{2}} dx }$ $3\displaystyle{ \int \frac{\hspace{2} 3{x}^{3}+12x+1 \hspace{2}}{\hspace{2} {x}^{2}+4 \hspace{2}} dx }$ $3\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} {x}^{2}- 4 \hspace{2}} dx }$ $3\displaystyle{\int \frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{ 4- 9{x}^{2} } \hspace{2}}dx }$ $3\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \( 3x+1 \) }^{2}+4 \hspace{2}}dx }$ $3\displaystyle{\int \frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{ {x}^{2}+5 } \hspace{2}}dx }$ $3\displaystyle{\int {5}^{x}dx }$ $3\displaystyle{ \displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \cos }^{2}2x \hspace{2}} }dx }$ $3\displaystyle{ \displaystyle{ \int { \tan }^{2}2x }dx }$ $3\displaystyle{\int \sin 3x\cos 5xdx }$ $3\displaystyle{ \displaystyle{ \int \sin 3x\sin 5x }dx }$ $3\displaystyle{ \displaystyle{ \int \cos 3x\cos 5x }dx }$ $3\displaystyle{ \displaystyle{ \int { \sin }^{2}2x }dx }$ $3\displaystyle{ \displaystyle{ \int { \cos }^{2}2x }dx }$ $3\displaystyle{ \displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \tan }^{2}2x \hspace{2}} }dx }$ $3\displaystyle{ \int { \( 3{x}^{2}- 5x+2 \) }^{2} \( 6x- 5 \) dx }$ $3\displaystyle{ \int x\sqrt{ 3x- 5 } dx }$ $3\displaystyle{\int \frac{\hspace{2}1\hspace{2}}{\hspace{2} 3x- 1 \hspace{2}}dx }$ $3\displaystyle{ \displaystyle{ \int \frac{\hspace{2} 6x- 5 \hspace{2}}{\hspace{2} 3{x}^{2}- 5x+2 \hspace{2}} }dx }$ $3\displaystyle{\int {e}^{ 3x }dx }$ $3\displaystyle{ \int \frac{\hspace{2} {e}^{ 2x } \hspace{2}}{\hspace{2} {e}^{ 2x }- 1 \hspace{2}} dx }$ $3\displaystyle{ \displaystyle{ \int \frac{\hspace{2} \log 2x \hspace{2}}{\hspace{2}x\hspace{2}} }dx }$ $3\displaystyle{\int \sin \( 5x+\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}3\hspace{2}} \) dx }$ $3\displaystyle{\int \cos \( 5x+\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}3\hspace{2}} \) xdx }$ $3\displaystyle{ \int \tan 2x dx }$ $3\displaystyle{\int { \sec }^{2} \( 5x+\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}3\hspace{2}} \) dx }$ $3\displaystyle{ \int {\text{\cos ec}}^{2}\left({ 5x+\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}3\hspace{2}} }\right)dx }$

3. ̒ϕȂD
4.  $3\displaystyle{\int _{1}^{2} \( {x}^{3}- 3{x}^{2}+\frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{x} \hspace{2}} \) dx }$ @@@@ $3\displaystyle{\int _{ \frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}} }^{4} \frac{\hspace{2}1\hspace{2}}{\hspace{2} 8x+3 \hspace{2}} dx}$ $3\displaystyle{ \int _{2}^{4} {e}^{ \frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}}x }dx }$ $3\displaystyle{\int _{ \frac{\hspace{2}1\hspace{2}}{\hspace{2}3\hspace{2}} }^{2} {8}^{x} dx}$ $3\displaystyle{\int _{ - \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}4\hspace{2}} }^{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} } \sin \( x+\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} \) dx}$ $3\displaystyle{\int _{ - \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}4\hspace{2}} }^{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} } \cos \( x+\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} \) dx }$ $3\displaystyle{\int _{ - \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}4\hspace{2}} }^{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} } { \sec }^{2} \( x+\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} \) dx }$ $3\displaystyle{\int _{ - \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}4\hspace{2}} }^{ - \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}6\hspace{2}} } { \text{\cos ec} }^{2} \( x+\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} \) dx }$ $3\displaystyle{\int _{1}^{ \sqrt{3} } \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \( x+1 \) }^{2}+3 \hspace{2}}dx }$ @@ $3\displaystyle{\int _{1}^{ \sqrt{2} } \frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{ 4- 2{x}^{2} } \hspace{2}}dx }$ $3\displaystyle{\int _{ - 3 }^{0} \frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{ {x}^{2}+16 } \hspace{2}}dx }$ @ @ @

5. ̕sϕ𕔕ϕ@pĉȂD
6.  $3\displaystyle{\int {x}^{3}{e}^{x}dx }$ $3\displaystyle{ \int 2x{e}^{ 2x } dx }$ $3\displaystyle{ \int x\sin x dx }$ $3\displaystyle{ \int x\cos x dx }$ $3\displaystyle{\int {e}^{ 2x }\sin x dx}$ $3\displaystyle{\int \sqrt{ {x}^{2}+5 }dx }$ $3\displaystyle{ \int \log 2x dx }$ $3\displaystyle{\int \log \( x+1 \) dx }$ $3\displaystyle{ \int 2\log \( 2x+1 \) dx }$ $3\displaystyle{\int { \( \log 2x \) }^{3}dx }$

7. ̕sϕȂD
8.  $3\displaystyle{\int \frac{\hspace{2}1\hspace{2}}{\hspace{2} \cos x \hspace{2}}dx }$ @ $3\displaystyle{\tan \frac{\hspace{2}x\hspace{2}}{\hspace{2}2\hspace{2}}=t}$ @ŒuĉȂD $3\displaystyle{\int \frac{\hspace{2}1\hspace{2}}{\hspace{2} \sin x \hspace{2}}dx }$ @ $3\displaystyle{\tan \frac{\hspace{2}x\hspace{2}}{\hspace{2}2\hspace{2}}=t}$ @ŒuĉȂD $3\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} \sin x+\cos x+1 \hspace{2}}dx }$ @ $3\displaystyle{\tan \frac{\hspace{2}x\hspace{2}}{\hspace{2}2\hspace{2}}=t}$ @ŒuĉȂD

9. ̕sϕ$3\displaystyle{ \int \sin x\cos x dx }$ ꂼ̏ŉȂD
10.  $3\displaystyle{2}$ {p̌pĉȂD $3\displaystyle{ \cos x=t }$ @ŒuĉȂD $3\displaystyle{ \sin x=t }$ @ŒuĉȂD $3\displaystyle{ \displaystyle{ \int { \( - \cos x \) }^{\prime }\cos x }dx }$ @ƍlϕpĉȂD $3\displaystyle{ \int \sin x{ \( \sin x \) }^{\prime } dx }$ @ƍlϕpĉȂB

11. ̐}`̏dS߂ȂD
12.  $3\displaystyle{ y=\frac{\hspace{2}3\hspace{2}}{\hspace{2}2\hspace{2}}x \( 0\leq x\leq 2 \) }$ $3\displaystyle{x}$ ň͂܂ꂽ}`̏dS߂ȂD Ȑ$3\displaystyle{y=\frac{\hspace{2}3\hspace{2}}{\hspace{2}4\hspace{2}}{x}^{2} \( 0\leq x\leq 2 \) }$ $3\displaystyle{x}$Ɉ͂܂ꂽ}`̏dS߂ȂD $3\displaystyle{y=\frac{\hspace{2}1\hspace{2}}{\hspace{2}4\hspace{2}}x \( 0\leq x\leq 4 \) }$ $3\displaystyle{x}$Ɉ͂܂ꂽ}`̏dS߂ȂD $3\displaystyle{ y=x \( 0\leq x\leq 3 \) }$ $3\displaystyle{x}$Ɉ͂܂ꂽ}`̏dS߂ȂD Ȑ$3\displaystyle{y=\frac{\hspace{2}1\hspace{2}}{\hspace{2} 16 \hspace{2}}{x}^{2} \( 0\leq x\leq 4 \) }$$3\displaystyle{x}$Ɉ͂܂ꂽ}`̏dS߂ȂD $3\displaystyle{ y=\frac{\hspace{2}3\hspace{2}}{\hspace{2}2\hspace{2}}x \( 0\leq x\leq 2 \) }$ $3\displaystyle{x}$ ň͂܂ꂽ}`$3\displaystyle{x}$̎$3\displaystyle{1}$ ]Ăł闧̂̏dS߂ȂD $3\displaystyle{1\leq x\leq 4}$ ͈̔͂ŁA$3\displaystyle{y=x}$ ƋȐ$3\displaystyle{y={x}^{2}- 4x+4}$ ň͂܂ꂽ}`̏dS߂ȂD

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