-d x-x-34 - 5x-16 - 5-A- 5-4x-3-x-11 - 5-cB- x-1-x-31 - 5-c- x-36 - 5x-14 - 5- -D- x-3x-11 - 5- c

The correct option is A 5/4 ( x 3/x+1 )^1/5+cPut t=x 3/x+1 ⇒ dx=(x+1)^2 dt/4 ...

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Standard Formulae - 2

∫d x/x-34 / 5...

Question

$\int \frac{d x}{(x - 3)^{4 / 5} (x + 1)^{6 / 5}} =$

((x - 3) (x + 1))^{1 / 5} + c

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\frac{5}{4} {(\frac{x - 3}{x + 1})}^{1 / 5} + c

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{(\frac{x + 1}{x - 3})}^{1 / 5} + c

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(x - 3)^{6 / 5} (x + 1)^{4 / 5} + c

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Solution

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\int \frac{d x}{(x - 3)^{(4 / 5)} (x + 1)^{6 / 5}} =

\int \frac{d x}{(x - 3)^{(4 / 5)} (x + 1)^{6 / 5}} =

x .

3^{x} \times 3^{- 2} = 3^{2}

5^{- 3} \div 5^{x} = 5^{2}

{(\frac{11}{5})}^{- 5} \times {(\frac{11}{5})}^{- 2} = {(\frac{11}{5})}^{x - 9}

Solve the equations:

(i) 5x = 3x + 24;

(ii) 8t + 5 = 2t − 31;

(iii) 7x − 10 = 4x + 11;

(iv) 4z + 3 = 6 + 2z;

(v) 2x − 1 = 14 − x;

(vi) 6x + 1 = 3(x − 1) + 7;

(vii) ;

(viii) ;

(ix) 3(x + 1) = 12 + 4 (x − 1);

(x) 2x − 5 = 3(x − 5);

(xi) 6(1 − 4x) + 7(2 + 5x) = 53;

(xii) 3(x + 6) + 2 (x + 3) = 64;

(xiii) ;

(xiv) .

x^{- 4} + x^{- 5}

- (4 x^{- 5} + 5 x^{- 6})

\int \frac{5 x^{4} + 4 x^{5}}{(x^{5} + x + 1)^{2}} d x

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