Question

please give answer it is important for me ​

Answer 1

Explanation:

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Answer 2

Explanation :

$\green{ \displaystyle \int \tt \dfrac{ \sqrt[5]{x {}^{2} } }{ \sqrt{x {}^{ \dfrac{14}{5} } }} dx} \\ \\ \\ \displaystyle \longrightarrow \tt\int \dfrac{ \bigg(x {}^{2} \bigg) {}^{ \dfrac{1}{5} } }{ \bigg(x {}^{ \dfrac{14}{5}} \bigg) {}^{ \dfrac{1}{2} } } dx \\ \\ \\ \displaystyle \longrightarrow \tt\int \dfrac{x {}^{ \dfrac{2}{5} } }{x {}^{ \dfrac{7}{5} } } dx \\ \\ \\ \displaystyle \longrightarrow \tt\int x {}^{ \dfrac{2}{5} - \dfrac{7}{5} } dx \\ \\ \\ \displaystyle \longrightarrow \tt\int x {}^{ \dfrac{ -5 }{5} } dx \\ \\ \\ \displaystyle \longrightarrow \tt\int x {}^{ \not\dfrac{ -5 }{5} } dx \\ \\ \\ \displaystyle \longrightarrow \tt\int x {}^{ - 1} dx \\ \\ \\ \displaystyle \longrightarrow \tt\int {\dfrac{1}{x} }dx \\ \\ \\ \displaystyle \longrightarrow\tt\red{in |x| +c}$

Know to more :

• Power rule.

$\bull\tt \int x {}^{n} .dx \: \rightarrow \: \dfrac{x {}^{n + 1} }{n + 1} + c$

• Multiplication by constant (c).

$\bull\tt \int c \: f(x).dx \: \rightarrow \: c \int f(x).dx$

• Sum rule.

$\bull\tt \int (f + g)dx \rightarrow \: \int fdx \: + \: \int gdx$

• Difference rule.

$\bull \tt \int (f - g)dx \rightarrow \: \int fdx \: - \: \int gdx$