Question

solve correct answer. ​

Answer 1

According to the power rule,

$\bold \red{ \int x {}^{n} .dx} \: \rightarrow \bold \green{ \dfrac{x {}^{n + 1} }{n + 1} + c}$

Case (I), ㅤ$\sf \int x {}^{3} .dx$

$\mapsto \sf \: \dfrac{x {}^{3 + 1} }{3 + 1} + c$

$\mapsto { \boxed{ \sf{\dfrac{x {}^{4} }{4} + c}}} \: \bigstar$

ㅤㅤㅤㅤㅤ

Case (II), ㅤ$\sf \int x {}^{9} .dx$

$\mapsto \sf \: \dfrac{x {}^{9 + 1} }{9 + 1} + c$

$\mapsto{ \boxed{ \sf{ \frac{x {}^{10} }{10} + c}}} \: \bigstar$

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Case (III), ㅤ $\sf\int x {}^{2} .dx$

$\mapsto \sf \: \dfrac{x {}^{2 + 1} }{2 + 1} + c$

$\mapsto{ \boxed{ \sf{ \frac{x {}^{3} }{3} + c}}} \: \bigstar$

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Answer 2

Answer

(I), ㅤ$\sf \int x {}^{3} .dx$

$\mapsto \sf \: \dfrac{x {}^{3 + 1} }{3 + 1} + c$

$\mapsto { \boxed{ \sf{\dfrac{x {}^{4} }{4} + c}}} \: \bigstar$

ㅤㅤㅤㅤㅤ

(II), ㅤ$\sf \int x {}^{9} .dx$

$\mapsto \sf \: \dfrac{x {}^{9 + 1} }{9 + 1} + c$

$\mapsto{ \boxed{ \sf{ \frac{x {}^{10} }{10} + c}}} \: \bigstar$

ㅤㅤㅤㅤㅤ

(III), ㅤ $\sf\int x {}^{2} .dx$

$\mapsto \sf \: \dfrac{x {}^{2 + 1} }{2 + 1} + c$

$\mapsto{ \boxed{ \sf{ \frac{x {}^{3} }{3} + c}}} \: \bigstar$

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