Question

plz solve it................ ​

Answer 1

GIVEN :–

• A function $\: \: { \bold{ 2x(1 - {x}^{ - 3} )}} \: \:$

TO FIND :–

• Integration = ?

SOLUTION :–

• Let the function –

$\\ \implies{ \bold{ I = \int 2x(1 - {x}^{ - 3} ).dx}}$

$\\ \implies{ \bold{ I = \int \{2x -(2x ) {x}^{ - 3} \}.dx}}$

$\\ \implies{ \bold{ I = 2 \int (x - {x}^{ - 2}).dx}}$

• Using identity –

$\\ \: \: \blacktriangleright \: \: { \bold{ \int {x}^{n} .dx = \dfrac{ {x}^{n + 1} }{n + 1} }}$

• So that –

$\\ \implies{ \bold{ I = 2 \left( \dfrac{{x}^{1 + 1} }{1 + 1} - \dfrac{{x}^{ - 2 + 1}}{ - 2 + 1} \right)+c}}$

$\\ \implies{ \bold{ I = 2 \left( \dfrac{{x}^{2} }{2} - \dfrac{{x}^{ - 1}}{ - 1} \right) + c}}$

$\\ \implies \large{ \boxed{ \bold{ I = \left( {{x}^{2} } + \dfrac{2}{ x} \right) + c}}}$

$\\ \rule{220}{2}$

OTHER IDENTITY :–

$\\ \: \: \blacktriangleright \: \: { \bold{ \int [K.F(x)].dx = K \int F(x).dx }}$

Answer 2

Answer:

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