∫ x n d x = \int_{ }^{ }x^{^n}dx= ∫ x n d x =

1 n + 1 x n + 1 + C \frac{1}{n+1}x^{n+1}+C n + 1 1 x n + 1 + C

1 n x n + 1 + C \frac{1}{n}x^{n+1}+C n 1 x n + 1 + C

n x n + 1 + C nx^{n+1}+C n x n + 1 + C

n x n − 1 + C nx^{n-1}+C n x n − 1 + C

∫ 7 d x = \int_{ }^{ }7dx= ∫ 7 d x =

1 7 x + C \frac{1}{7}x+C 7 1 x + C

Jika f ( x ) = x 3 n f\left(x\right)=x^{3n} f ( x ) = x 3 n , untuk setiap n n n dan n ≠ − 1 3 n\ne-\frac{1}{3} n  = − 3 1 maka ∫ f ( x ) d x \int_{ }^{ }f\left(x\right)\ dx ∫ f ( x ) d x adalah ....

1 3 n + 1 x ( 3 n + 1 ) + C \frac{1}{3n+1}x^{\left(3n+1\right)}+C 3 n + 1 1 x ( 3 n + 1 ) + C

1 3 n x 3 n + C \frac{1}{3n}x^{3n}+C 3 n 1 x 3 n + C

1 4 n x 4 n + C \frac{1}{4n}x^{4n}+C 4 n 1 x 4 n + C

x ( 3 n + 1 ) + C x^{\left(3n+1\right)}+C x ( 3 n + 1 ) + C

1 n + 1 x ( n + 1 ) + C \frac{1}{n+1}x^{\left(n+1\right)}+C n + 1 1 x ( n + 1 ) + C

∫ 1 2 x x d x \int_{ }^{ }\ \frac{1}{2x\sqrt{x}}\ dx ∫ 2 x x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1 d x adalah ....

− 1 x + C -\frac{1}{\sqrt{x}}+C − x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1 + C

− 1 x x + C -\frac{1}{x\sqrt{x}}+C − x x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1 + C

1 x + C \frac{1}{\sqrt{x}}+C x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1 + C

− 2 x + C -\frac{2}{\sqrt{x}}+C − x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 2 + C

− 1 2 x + C -\frac{1}{2\sqrt{x}}+C − 2 x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1 + C

Hasil dari ∫ sin 3x cos 2x dx =....

− 1 / 10 cos 5x − 1 / 2 cos x + C

− 1 / 5 cos 5x + 1 / 2 cos x + C

−sin 1 / 2 x − 5 sin 5 / 2 x + C

Integral

Authored by Nesy Widyastuti

Mathematics

3rd Grade

CCSS covered

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FILL IN THE BLANK QUESTION

2 mins • 10 pts

∫₁² (12x² + 4x³)dx

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Jika ada materi yang kurang dipahami, saya akan ...

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MULTIPLE SELECT QUESTION

30 sec • 1 pt

saya sudah paham sub materi ?

integral tertentu

integral tak tentu

luas daerah

volume benda putar

MULTIPLE CHOICE QUESTION

30 sec • 10 pts

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

rumus umum dari integral diatas adalah ....

n*x^n-1 + C

(n+1)*xⁿ⁺¹ + C

¹/_n-1 * x^n-1 + C

¹/_n+1 * xⁿ⁺¹ + C

MULTIPLE CHOICE QUESTION

30 sec • 5 pts

MULTIPLE CHOICE QUESTION

30 sec • 10 pts

∫ (8x³ - 3x² +6x + 5) dx=

2x⁴+3x³+c

2x⁴ - x³ + x² + 5x + c

4x²+ x+c

2x⁴ - x³ + 3x² + 5x + c

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Integral

∫₁² (12x² + 4x³)dx

Jika ada materi yang kurang dipahami, saya akan ...

saya sudah paham sub materi ?

rumus umum dari integral diatas adalah ....

∫ (8x3 - 3x2 +6x + 5) dx=

rumus umum dari integral diatas adalah...

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∫ (8x³ - 3x² +6x + 5) dx=