Question

PLS SOLVE THIS INTEGRATION QUESTION ​

Answer 1

$\bf \: we \: have \:$

$\sf \to \: \int \bigg( \dfrac{ - 6}{ {x}^{3} } + \dfrac{6}{ {x}^{4} } \bigg)dx$

$\bf \: We \: This \: identities \: of \: Intergration </p><p>$

$\sf \to\int(a \pm \: b)dx = \int(a)dx \pm \int(b)dx$

$\bf \: Now$

$\sf \to \: \int \bigg( \dfrac{ - 6}{ {x}^{3} } \bigg)dx + \int\bigg(\dfrac{6}{ {x}^{4} } \bigg)dx$

$\sf \to \: - 6 \int \bigg( \dfrac{ 1}{ {x}^{3} } \bigg)dx + 6\int\bigg(\dfrac{1}{ {x}^{4} } \bigg)dx$

$\sf \to \: - 6 \int( {x}^{ - 3} )dx + 6 \int(x {}^{ - 4} )dx$

$\sf \to- 6 \bigg(\dfrac{ x {}^{ - 3 + 1} }{ - 3 + 1} \bigg) + 6 \bigg( \dfrac{ {x}^{ - 4 + 1} }{ - 4 + 1} \bigg) + c$

$\sf \to \: - 6 \bigg( \dfrac{ - x {}^{ - 2} }{2} \bigg) - 6 \bigg( \dfrac{ {x}^{ - 3} }{3} \bigg) + c$

$\sf \to \: \dfrac{6}{2 {x}^{2} } - \dfrac{6}{3 {x}^{3} } + c$

$\sf \to \: \dfrac{3}{ {x}^{2} } - \dfrac{2}{ {x}^{3} } + c$

$\bf \: Answer$

$\sf \to \: \dfrac{3}{ {x}^{2} } - \dfrac{2}{ {x}^{3} } + c$