Find the integral of -2 x12-5 x9-x5-x3-13 d x-

I=∫2x^12+5x^9/(x^5 + x^3 + 1)^3dx =∫2x^12+5x^9/x^15 ( 1+1/x^2+1/x^5 )^3dx = ∫2/x^3 + 5/x^6/ ( 1+1/x^2+1/x^5 )^3dx = ∫ d ( 1+1/x^2+1/x^5 )/ ( 1+1/x^2+1/x^5 ...

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Byju's Answer

Standard XII

Mathematics

Theorems on Integration

Find the inte...

Question

Find the integral of $\int \frac{2 x^{12} + 5 x^{9}}{(x^{5} + x^{3} + 1)^{3}} d x$ .

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Solution

$I = \int \frac{2 x^{12} + 5 x^{9}}{(x^{5} + x^{3} + 1)^{3}} d x = \int \frac{2 x^{12} + 5 x^{9}}{x^{15} {(1 + \frac{1}{x^{2}} + \frac{1}{x^{5}})}^{3}} d x = \int \frac{\frac{2}{x^{3}} + \frac{5}{x^{6}}}{{(1 + \frac{1}{x^{2}} + \frac{1}{x^{5}})}^{3}} d x = \int \frac{- d (1 + \frac{1}{x^{2}} + \frac{1}{x^{5}})}{(1 + \frac{1}{x^{2}} + \frac{1}{x^{5}})} = \frac{1}{2} {(1 + \frac{1}{x^{2}} + \frac{1}{x^{5}})}^{2} = \frac{x^{10}}{2} (x^{5} + x^{3} + 1)^{2} + C$

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Similar questions

Q. The integral

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

is equal to?

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

is equal to
(where

C

is constant of integration)

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

is equal to

The integral $\int \frac{2 x^{12} + 5 x^{9}}{(x^{5} + x^{3} + 1)^{3}}$ dx is equal to : where C is an arbitary constant.

Q. The intergral

\int \frac{2 x^{12} + 5 x^{9}}{(x^{5} + x^{3} + 1)^{3}}

dx is equal to :

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Find the integral of ∫2x12+5x9(x5+x3+1)3dx.

I=∫2x12+5x9(x5+x3+1)3dx=∫2x12+5x9x15(1+1x2+1x5)3dx=∫2x3+5x6(1+1x2+1x5)3dx=∫−d(1+1x2+1x5)(1+1x2+1x5)=12(1+1x2+1x5)2=x102(x5+x3+1)2+C

Find the integral of $\int \frac{2 x^{12} + 5 x^{9}}{(x^{5} + x^{3} + 1)^{3}} d x$ .