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<b>CHUYÊN ĐỀ TÍCH PHÂN LTĐH DIỄN ĐÀN ONLUYENTOAN.VN</b>
<b>Câu I.</b> Tính các tích phân sau
1. I=
Z π
6
0
4 cos 5xsin 2x
1+tanxtanx
2
dx
2. I=
Z 1
0
x.ln(x2+x+1)dx
3. I=
Z 1
0
(x2+2x+2)ex
x2<sub>+</sub><sub>4</sub><sub>x</sub><sub>+</sub><sub>4</sub> dx
4. I=
Z π<sub>2</sub>
0
ln(1+cosx)
sinx+1
sinx+1 dx
5. I=
Z 3
2
√
x+2
x+√x2−4dx
6. I=
Z e
1
e
lnxln(x2+1)
x dx
7. I=
Z π<sub>3</sub>
0
x2
(xsinx+cosx)2dx
8. I=
Z π
2
0
cosx
(√3 sinx+cosx)3dx
9. I=
Z 6
2
dx
2x+1+√4x+1
10. I=
Z e
1
1−x(ex−1)
x(1+xex<sub>ln</sub><sub>x</sub><sub>)</sub>dx
<b>Câu II.</b> Tính các tích phân sau
1. I=
Z
√
3
0
x5+2x2
√
x2<sub>+</sub><sub>1</sub>dx
2. I=
Z
√
3
0
x2+2
√
x2<sub>+</sub><sub>1</sub>dx
3. I=
Z 1
0
1+ (2+x)xe2x
1+xex dx
4. I=
Z π
2
π
3
cosx+2
sin 2x+2 sinxdx
5. I=
Z e
1
3
p
e3x<sub>+</sub><sub>1</sub><sub>e</sub>2x<sub>dx</sub>
6. I=
Z 3<sub>2</sub>
1
2
4x−3
x+2
e2(x+4x3)<sub>d</sub><sub>x</sub>
7. I=
Z π<sub>6</sub>
0
dx
cos3<sub>x</sub>
8. I=
Z e
1
lnx−1
x2<sub>−</sub><sub>(</sub><sub>ln</sub><sub>x</sub><sub>)</sub>2dx
9. I=
Z π
2
0
sinx.(1+14xcosx)−xsin 4x
7−2 cos 2x dx.
10. I=
Z π<sub>2</sub>
0
sinx
sin3x+cos3<sub>x</sub>dx
<b>Câu III.</b> Tính các tích phân sau
1. I=
Z e
1
log3<sub>2</sub>x
p
1+3 ln2x
dx
2. I=
Z 1
0
x6
1+x12dx
3. I=
Z −1
−3
dx
(x2+6x+13)2
4. I=
Z 1
0
p
x4<sub>+</sub><sub>3</sub><sub>x</sub>3<sub>dx</sub>
5. I=
Z 2
1
(x−3)dx
x(x+1)(x+2)
6. I=
Z 2
1
x2−1
x4<sub>+</sub><sub>1</sub>dx
7. I=
Z 3π<sub>4</sub>
π
4
3
p
sin3x−sinx
sin3x cotxdx
8. I=
Z 1
−1
x2ln(1+x2)
2x<sub>+</sub><sub>1</sub> dx
9. I=
Z π<sub>2</sub>
0
x
sinx+cosxdx
10. I=
Z 3
1
(x−2)
r
x
4−xdx
<b>Câu IV.</b> Tính các tích phân sau
1. I=
Z e
1
√
xlnx
1+lnx
2
dx
2. I=
Z π<sub>2</sub>
0
sin 4x
cos 3xdx
3. I=
Z π
4
0
1
(1+sinx)cos2<sub>x</sub>dx
4. I=
Z <sub>xe</sub>x
ex+1dx
</div>
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5. I=
Z π
2
0
dx
1+sinx
6. I=
Z e
1
xx.(lnx+1)dx
7. I=
Z π
3
0
x.ex(4+4(sinx+cosx) +sin 2x)
(1+cosx)2 dx
8. I=
Z ln 2
0
(x2+2)e2x+x2(1−ex)−ex
e2x<sub>−</sub><sub>e</sub>x<sub>+</sub><sub>1</sub> dx
9. I=
Z 4
1
xlnxdx
(x2+1)2
10. I=
Z 5
2
(x−1)x
(x+1)2+x2
dx
<b>Câu V.</b> Tính các tích phân sau
1. I=
Z π<sub>2</sub>
−π
2
x+cosx
4−sin2x
2. I=
Z 1
−1
ex−e−xsinxdx
3. I=
Z 2
√
2
√
3
√
x2<sub>+</sub><sub>1</sub>
x2 dx
4. I=
√
3
3
Z
0
x
1−x4ln
3−x2
2
dx
5. I=
Z π<sub>4</sub>
0
2x+cos2x
1+sin 2x dx
6. I=
Z 1<sub>2</sub>
0
ln(1−x)
2x2<sub>−</sub><sub>2</sub><sub>x</sub><sub>+</sub><sub>1</sub>dx
7. I=
Z π<sub>2</sub>
π
4
xcos4(π−x)
cos4 <sub>x</sub><sub>−</sub>3π
2
+sin4 x+3π
2
−1dx
8. I=
Z e
1
xlnx
(1+x2)2dx
9. I=
Z e3
1
2 lnx+1
x(√lnx+1+1)dx
10. I=
Z π
2
0
cos99x
cos99<sub>x</sub><sub>+</sub><sub>sin</sub>99<sub>x</sub>dx
<b>Câu VI.</b> Tính các tích phân sau
1. I=
Z
√
3
1
√
3
1
1+x2<sub>+</sub><sub>x</sub>2010<sub>+</sub><sub>x</sub>2012dx
2. I=
Z
√
8
√
3
x3lnx
√
x2<sub>+</sub><sub>1</sub>dx
3. I=
π
2
Z
0
sinx(1+14xcosx)−xsin 4x
7−2 cos 2x dx
4. I=
Z π
4
−π
4
sin2xdx
cos4<sub>x</sub><sub>(</sub><sub>tan</sub>2<sub>x</sub><sub>−</sub><sub>2 tan</sub><sub>x</sub><sub>+</sub><sub>5</sub><sub>)</sub>
5. I=
Z 1
0
ln(1+x)dx
x2<sub>+</sub><sub>1</sub>
6. I=
Z π<sub>2</sub>
0
dx
sinx+2 cosx
7. I=
Z π<sub>2</sub>
π
3
1
sin 2x−2 sinxdx
8. I=
Z 2
1
x2−1
(x2−x+1)(x2+3x+1)dx
9. I=
2
Z
1
x4+1
x6<sub>+</sub><sub>1</sub>dx
10. I=
Z 1
0
3e2x−5ex+4
ex<sub>+</sub><sub>1</sub> dx
<b>Câu VII.</b> Tính các tích phân sau
1. I=
Z π
0
xsinx
1+cos2xdx
2. I=
Z <sub>12</sub>π
0
tan2x−3
3 tan2<sub>x</sub><sub>−</sub><sub>1</sub>dx
3. I=
Z 1
0
x−e2x
x.ex<sub>+</sub><sub>e</sub>2xdx
4. I=
Z π<sub>4</sub>
0
x.tan2xdx
5. I=
π
2
Z
−π
2
sin x+π
2
1−sinx+√2−cos2<sub>x</sub>d(x)
6. I=
Z π<sub>2</sub>
π
4
cotx+1
ex<sub>sin</sub><sub>x</sub><sub>+</sub><sub>1</sub>dx
7. I=
Z π
2
0
cos3xdx
2−sin 2x
8. I=
Z e
1
xlnx
√
1+x2dx
9. I=
Z 1
−1
1
x2<sub>+</sub><sub>x</sub><sub>+</sub><sub>1</sub><sub>+</sub>√<sub>x</sub>4<sub>+</sub><sub>3</sub><sub>x</sub>2<sub>+</sub><sub>1</sub>dx
10. I=
Z 4
0
p
x2<sub>−</sub><sub>6</sub><sub>x</sub><sub>+</sub><sub>9</sub><sub>dx</sub>
</div>
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<b>Câu VIII.</b> Tính các tích phân sau
1. I=
2
Z
1
x
1− 1
x4
ln(x2+1)−lnxdx
2. I=
Z 2
1
x3√x3<sub>+</sub><sub>8</sub><sub>+ (</sub><sub>3</sub><sub>x</sub>3<sub>+</sub><sub>5</sub><sub>x</sub>2<sub>)</sub><sub>ln</sub><sub>x</sub>
x dx
3. I=
2
Z
0
xdx
√
2+x+√2−x
4. I=
Z e
1
xlnx 1
x2 <sub>1</sub><sub>+</sub>√<sub>3 ln</sub><sub>x</sub><sub>+</sub><sub>1</sub>−1
!
dx
5. I=
Z π<sub>2</sub>
0
cosx√1−sinx
sinx+3 dx
6. I=
Z 1
0
1+√4<sub>x</sub>
1+√xdx
7. I=
Z π
4
0
tanx.ln(cosx)
cosx dx
8. I=
Z π<sub>2</sub>
0
cosx
1+sin 2xdx
9. I=
Z π
6
0
1
sin4x+cos4<sub>x</sub>dx
10. I=
Z 2
1
r
1
x+1dx
<b>Câu IX.</b> Tính các tích phân sau
1. I=
Z π<sub>6</sub>
0
tanx+xtan 2x
cos2<sub>2</sub><sub>x</sub> dx
2. I=
Z π
0
x2cos2x−xsinx−cosx−1
(1+xsinx)2
3. I=
Z π
2
π
4
sinx+cosx
4+cos 2x.tan(x−π
4)
dx
4. I=
π
2
Z
0
sin 3x
√
1+3 cosxdx
5. I=
Z e
1
(1+lnx)lnx
(1+x+lnx)3dx
6. I=
π
4
Z
0
tanx
cosx√cos2<sub>x</sub><sub>+</sub><sub>1</sub>
7. I=
Z 1
0
dx
1+√x+√x+1
8. I=
Z π
4
0
(x+sin22x)cos 2xdx
9. I=
Z 0
1−√3
dx
(x−1)√x2<sub>−</sub><sub>2</sub><sub>x</sub><sub>+</sub><sub>2</sub>
10. I=
Z 2
0
ex2(x+2)
x2<sub>e</sub>x<sub>−</sub><sub>9</sub> dx
<b>Câu X.</b> Tính các tích phân sau
1. I=
Z e
1
sin 2x+lnex+xsin 2xlnx
1+xlnx dx
2. I=
Z e
1
lnx
x√1+3 lnxdx
3. I=
Z 1
0
e
√
3x+1
dx
4. I=
Z π<sub>3</sub>
π
4
1
sinx.cos3<sub>x</sub>dx
5. I=
Z 2
1
xdx
3
√
x+1−√x+1
6. I=
Z π<sub>2</sub>
0
1+sinx
1+cosxe
x<sub>dx</sub>
7. I=
Z e
1
1−lnx
x(x+lnx)dx
8. I=
Z 3
1
r
x
4−xdx
9. I=
Z π<sub>2</sub>
0
ex.sinx
1+sin 2xdx
10. I=
Z 1
0
2x+1
x4<sub>+</sub><sub>2</sub><sub>x</sub>3<sub>+</sub><sub>3</sub><sub>x</sub>2<sub>+</sub><sub>2</sub><sub>x</sub><sub>−</sub><sub>3</sub>dx
</div>
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