∫ x + 1 d x \int_{ }^{ }\sqrt{x+1}dx ∫ x + 1 <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"> d x

2 ( x + 1 ) 3 2 3 + C \frac{2\left(x+1\right)^{\frac{3}{2}}}{3}+C 3 2 ( x + 1 ) 2 3 + C

( x + 1 ) 1 2 + C \left(x+1\right)^{\frac{1}{2}}+C ( x + 1 ) 2 1 + C

3 ( x + 1 ) 3 2 2 + C \frac{3\left(x+1\right)^{\frac{3}{2}}}{2}+C 2 3 ( x + 1 ) 2 3 + C

3 2 x + 1 + C \frac{3}{2}\sqrt{x+1}+C 2 3 x + 1 <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"> + C

Integration by Substitution part 1

Authored by Mehnaz Jawed

Mathematics

12th Grade - University

Used 17+ times

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10 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\int_{ }^{ }\left(2x\right)\left(x^2-5\right)^3$

$4\left(x^2-5\right)^4$

$\frac{\left(x^2-5\right)^4}{4}$

$\frac{1}{2}\left(x^2-5\right)^4$

$\frac{\left(2x\right)\left(x^2-5\right)^4-}{4}$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\int_{ }^{ }3x^2\left(x^3+5\right)^7$

$\frac{\left(x^4+5\right)^8}{8}+C$

$\frac{\left(x^3+5\right)^8}{8}+C$

$\int3x^2\left(\frac{\left(x^3+5\right)^8}{8}\right)^{ }+C$

$\frac{3x^2}{8}+C$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\int_{ }^{ }\left(x^2+2\right)^5x\ dx$

$\frac{\left(x^2+2\right)^6}{12}+C$

$^{\frac{5\left(x^2+2\right)^4}{4}}+C$

$\frac{2\left(x^2+2\right)^6}{6}+C$

$\frac{\left(2x\right)^6}{6}+C$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\int x^2\left(x^3-5\right)^{\frac{2}{3}}dx$

$\frac{3\left(x^3-5\right)^{\frac{5}{3}}}{5}+C$

$\frac{\left(x^3-5\right)^{\frac{5}{3}}}{5}+C$

$\frac{9\left(x^3-5\right)^{\frac{5}{3}}}{5}+C$

$\frac{5\left(x^3-5\right)^{\frac{5}{3}}}{9}+C$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\int_{ }^{ }\sqrt{x^5-9}\left(x^4\right)dx$

$\frac{2\left(x^5-9\right)^{\frac{3}{2}}}{3}+C$

$\frac{10\left(x^5-9\right)^{\frac{3}{2}}}{3}+C$

$\frac{\left(x^5-9\right)^{\frac{3}{2}}}{\frac{3}{2}}+C$

$\frac{2}{15}\left(x^5-9\right)^{\frac{3}{2}}+C$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\int_{ }^{ }\sqrt{x^3-3x}\left(x^2-1\right)dx$

$\frac{2}{9}\left(x^3-3x\right)^{\frac{3}{2}}+C$

$\frac{2}{3}\left(x^3-3x\right)^{\frac{3}{2}}+C$

$\frac{3}{2}\left(x^3-3x\right)^{\frac{3}{2}}+C$

$\sqrt{x^3-3x}\left(2x\right)+C$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\int_{ }^{ }\left(x^4+2x^2-4x\right)\left(x^3+x-1\right)dx$

$\frac{\left(x^4+2x^2-4x\right)^2}{2}+C$

$\frac{\left(x^4+2x^2-4x\right)^2}{8}+C$

$2\left(x^4+2x^2-4x\right)^2+C$

$8\left(x^4+2x^2-4x\right)^2+C$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\int_{ }^{ }\left(x^3-3x^2-9x\right)^3\left(x^2-2x-3\right)dx$

$\frac{1}{4}\left(x^3-3x^2-9\right)^4+C$

$4\left(x^3-3x^2-9\right)^4+C$

$\frac{1}{12}\left(x^3-3x^2-9\right)^4+C$

$\frac{1}{2}\left(x^2-2x-3\right)^2+C$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\int_{ }^{ }\sqrt{x+1}dx$

$\left(x+1\right)^{\frac{1}{2}}+C$

$\frac{3\left(x+1\right)^{\frac{3}{2}}}{2}+C$

$\frac{2\left(x+1\right)^{\frac{3}{2}}}{3}+C$

$\frac{3}{2}\sqrt{x+1}+C$

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int_{ }^{ }\sqrt{\left(x^5-5\right)^3}\left(x^4\right)dx$

$\frac{2}{15}\left(x^5-5\right)^{\frac{3}{2}}+C$

$\frac{2}{3}\left(x^5-5\right)^{\frac{3}{2}}+C$

$\frac{2}{5}\left(x^5-5\right)^{\frac{5}{2}}+C$

$\frac{2}{25}\left(x^5-5\right)^{\frac{5}{2}}+C$

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Integration by Substitution part 1

∫(2x)(x2−5)3\int_{ }^{ }\left(2x\right)\left(x^2-5\right)^3∫​(2x)(x2−5)3

∫3x2(x3+5)7\int_{ }^{ }3x^2\left(x^3+5\right)^7∫​3x2(x3+5)7

∫(x2+2)5x dx\int_{ }^{ }\left(x^2+2\right)^5x\ dx∫​(x2+2)5x dx

∫x2(x3−5)23dx\int x^2\left(x^3-5\right)^{\frac{2}{3}}dx∫x2(x3−5)32​dx

∫x5−9(x4)dx\int_{ }^{ }\sqrt{x^5-9}\left(x^4\right)dx∫​x5−9​(x4)dx

∫x3−3x(x2−1)dx\int_{ }^{ }\sqrt{x^3-3x}\left(x^2-1\right)dx∫​x3−3x​(x2−1)dx

∫(x4+2x2−4x)(x3+x−1)dx\int_{ }^{ }\left(x^4+2x^2-4x\right)\left(x^3+x-1\right)dx∫​(x4+2x2−4x)(x3+x−1)dx

∫(x3−3x2−9x)3(x2−2x−3)dx\int_{ }^{ }\left(x^3-3x^2-9x\right)^3\left(x^2-2x-3\right)dx∫​(x3−3x2−9x)3(x2−2x−3)dx

∫x+1dx\int_{ }^{ }\sqrt{x+1}dx∫​x+1​dx

∫(x5−5)3(x4)dx\int_{ }^{ }\sqrt{\left(x^5-5\right)^3}\left(x^4\right)dx∫​(x5−5)3​(x4)dx

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$\int_{ }^{ }\left(2x\right)\left(x^2-5\right)^3$

$\int_{ }^{ }3x^2\left(x^3+5\right)^7$

$\int_{ }^{ }\left(x^2+2\right)^5x\ dx$

$\int x^2\left(x^3-5\right)^{\frac{2}{3}}dx$

$\int_{ }^{ }\sqrt{x^5-9}\left(x^4\right)dx$

$\int_{ }^{ }\sqrt{x^3-3x}\left(x^2-1\right)dx$

$\int_{ }^{ }\left(x^4+2x^2-4x\right)\left(x^3+x-1\right)dx$

$\int_{ }^{ }\left(x^3-3x^2-9x\right)^3\left(x^2-2x-3\right)dx$

$\int_{ }^{ }\sqrt{x+1}dx$

$\int_{ }^{ }\sqrt{\left(x^5-5\right)^3}\left(x^4\right)dx$