Hitunglah integral -integral berikutintegral (x²+1)² per akar x
1. Hitunglah integral -integral berikutintegral (x²+1)² per akar x
Jawaban:
tertera pada gambar
Penjelasan dengan langkah-langkah:
tertera pada gambar
IntegrAL
∫(x² + 1)²/√x dx
= ∫(x⁴ + 2x² + 1)/x^1/2 dx
= ∫(x^7/2 + 2x^3/2 + x^-1/2) dx
= 1/(7/2 + 1) x^9/2 + 2/(3/2 + 1) x^5/2 + 1/(-1/2 + 1) x^1/2 + C
= 2/9 x^9/2 + 4/5 x^5/2 + 2x^1/2 + C
2. integral dari sin akar x / akar x
integral by u-subs
misal : u = √x = x^(1/2)
du = 1/2 x^(-1/2) dx = dx/2x^1/2 = dx/(2√x)
2 du = dx/√x
so,
= 2 int sin(u) du
= -2 cos(u) + C
= -2 cos(√x) + C
3. integral sin akar x per akar x ?
| sin√x d√x
= -1/2 cosx²
4. Integral X per akar X+1 = …
misalkan x + 1 = u
dx = du
x = u - 1
ganti x kedalam u
= {(u - 1) / √u } du
= {(u - 1) / u^½} du
= {(u - 1)u^-½} du
= {u^(1-½) - u^-½} du
= {u^½ - u^-½} du
= (1/(½+1))u^(1+½) - (1/(-½+1))u^(1-½) + C
= (1/(3/2))u^3/2 + (1/(½))u^½ + C
= (⅔)u√u + 2√u + C
= (⅔√u)(u + 3) + C
kembalikan u = x + 1
= ⅔{√(x+1)}(x + 1 + 3) + C
= ⅔{√(x+1)}(x + 4) + C
5. tentukan integral tak tentu: integral akar x (x^2-x)dx
InTegraL
∫ax^n dx = a/(n+1) . x^(n+1) + C
••
∫√x (x² - x) dx
= ∫(x^5/2 - x^3/2) dx
= 1/(7/2) . x^7/2 - 1/(5/2) . x^5/2 + C
= 2/7 x³ √x - 2/5 x² √x + C ✔
6. integral x akar x dx?
Semoga membantu.. ^_^Semoga membantu yy
..
7. Integral (akar x+1)(akar x+2) ?
integral
(√x+1)(√x+2)
=x+2√x+√x+2
=x+3√x+2
=x+3x^1/2+2
=1/2x^2+2x^3/2+2x+c
ket :^=pangkat
/=per
8. Integral dari akar x kurang 1 per akar x
itu yaa jawabannyaaa
9. Integral x akar x+1 adalah...
∫ x √(x+1) dx
u = x + 1 --> x = (u-1)
du = dx
∫x√(x+1) dx = ∫(u-1)(u) du
= ∫u² - u du
= ¹/₃ u³ - ¹/₂ u² + c
= ¹/₆ u² (2u - 3) +c
= ¹/₆ (x+1)² {2(x+1) - 3 } +c
= ¹/₆ (x+1)² (2x-1) + c
10. integral 1/akar x + akar x dx
Jawaban:
DX akar semLx jd FB mcxjgnvn♡(> ਊ <)♡_!:("&jvncjf11. integral e^x + akar x adalah
Jawab:
Penjelasan dengan langkah-langkah:
integral e
[tex]\tt \int\limits{e^{x}} \, dx = e^{x}[/tex]
soal
[tex]\tt \int\limits ({e^{x} + \sqrt{x}} )\, dx[/tex]
[tex]\tt= \int\limits ({e^{x} + {x}^{\frac{1}{2}} )\, dx[/tex]
[tex]\sf = e^{x} + \frac{2}{3} x\sqrt{x}+c[/tex]
12. Integral x^2 akar x?
inT x^2 akarx dx = inT x^(5/2) dx
=> 1/(5/2 + 1) x^(5/2 + 1) + C
=> 1/(7/2) X^(7/2) + C
=> 2/7 X^(7/2) + C
atau
=> 2/7 X^3 akarX + C
1/3x³
pangkat dinaikkan
13. integral dari x akar x
integral x^(3/2) dx = (2/5) x^(5/2) + c
= 2x^2* Vx / 5 + c
X akar x= x^3/2
Integral x^3/2 = 1/(3/2+1) x^(3/2+1)
=1/(5/2) x^(5/2)
=2/5 x^5/2
14. 1.Integral(1-3x kuadrat)dx 2.integral(8x pangkat3) dx 3.integral tiga akar x kuadrat - 4 akar x kuadrat 4.integral (x pangkat 3-1)kuadrat dx 5.integral (1+akar x)kuadrat per x akar 3 dx
Cman 1 dan 2 . selanjutny klw mau mudah. Lihat tabel integral
15. tentukan hasil pengintegralan dari notasi integral X AKAR X DX
Jawaban:
2/5 x^2 √x + C
Penjelasan dengan langkah-langkah:
penjelasan terlampir
semoga membantu
16. integral 2 per x akar x
akar - akaran ubi , toge
1 per Xpangat 2 Xpangkat3/2
17. integral 1 per x akar x
.
∫1/(x√x) dx
= ∫x^-3/2 dx
= 1/(-1/2) x^(-1/2) + C
= -1/(2√x) + C
∫ 1/x√x
∫ 1 x (x)⁻¹per²
u = x
du = 1 dx
x du = x dx
x ∫ u⁻¹per²
x.1/-1/2+1 u⁻¹per2⁺¹
x . 2 u^1/2
2x (x)^1/2
2x √x
18. integral x akar x DX
[tex] \int\limits {x \sqrt{x} } \, dx \\ = \int\limits {x . x^{ \frac{1}{2} } } \, dx \\ = \int\limits { x^{ \frac{3}{2} } } \, dx \\ = \frac{1}{ \frac{3}{2}+1 } x^{ \frac{3}{2} +1}+C\\ = \frac{1}{ \frac{5}{2} }x^{ \frac{5}{2}}+C \\ \bold{= \frac{2}{5} x^{ \frac{5}{2}} +C}[/tex]Int x^3/2 dx
= 1/(3/2+1) x^3/2+1 +C
= 1/5/2 x^5/2 +C
= 2/5 x^5/2 + C
19. hasil pengintegralan dari integral akar x-1 per x^2 dx adalah
Jawab:
Penjelasan dengan langkah-langkah:
20. Integral x bagi akar x dx
∫x/√x dx
= ∫x^1/2 dx
= 1/(3/2) x^3/2 + C
= (2/3)x√x + C
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