Integral Calculus jee mains questions | JEE Main Maths Integral Calculus Previous Year Question

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Q 31 :

If $\int \frac{2 x^{12} + 5 x^{9}}{{(1 + x^{3} + x^{5})}^{3}} d x = \frac{x^{m}}{ℓ {(1 + x^{3} + x^{5})}^{r}} + C$ , then $\frac{m + ℓ}{r} =$

(4)

$\int \frac{2 x^{12} + 5 x^{9}}{{(1 + x + x^{5})}^{3}} d x = \int \frac{2 x^{12} + 5 x^{9}}{x^{15} {(\frac{1}{x^{5}} + \frac{1}{x^{2}} + 1)}^{3}} d x = \int \frac{\frac{2}{x^{3}} + \frac{5}{x^{6}}}{{(\frac{1}{x^{5}} + \frac{1}{x^{2}} + 1)}^{3}} d x$

Put $\frac{1}{x^{2}} + \frac{1}{x^{5}} + 1 = t \Rightarrow \int \frac{- d t}{t^{3}} = \frac{1}{2 t^{2}} + c = \frac{1}{2 {(\frac{1}{x^{5}} + \frac{1}{x^{2}} + 1)}^{2}} + c = \frac{x^{10}}{2 {(1 + x^{3} + x^{5})}^{2}} + c$

$m = 10; r = 2; l = 2; \frac{m + l}{r} = 6$

Topic Question Set

Q 31 :

If $\int \frac{2 x^{12} + 5 x^{9}}{{(1 + x^{3} + x^{5})}^{3}} d x = \frac{x^{m}}{ℓ {(1 + x^{3} + x^{5})}^{r}} + C$ , then $\frac{m + ℓ}{r} =$

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Topic Question Set

Q 31 : If ∫2x12+5x9(1+x3+x5)3dx=xmℓ(1+x3+x5)r+C, then m+ℓr=

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Q 31 :

If $\int \frac{2 x^{12} + 5 x^{9}}{{(1 + x^{3} + x^{5})}^{3}} d x = \frac{x^{m}}{ℓ {(1 + x^{3} + x^{5})}^{r}} + C$ , then $\frac{m + ℓ}{r} =$