The inegral -3 x13-2 x11-2 x4-3 x2-14 d x is equal towhere C is a constant of integrationA- x4-62 x4-3 x2-13-CB- x12-62 x4-3 x2-13-CC- x12-2 x4-3 x2-13-CD- x-2 x4-3 x2-13-C

I=∫3x^13+2x^11(2x^4+3x^2+1)^4 dx =∫3x^13+2x^11x^16 ( 2+3x^2+1x^4 )^4 dx nbsp; =∫ ( 3x^3+2x^5 ) ( 2+3x^2+1x^4 )^4 dx nbsp; Let nbsp; nbsp;2+3x^2+1x^4 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Integration by Substitution

The inegral ∫...

Question

The inegral $\int \frac{3 x^{13} + 2 x^{11}}{(2 x^{4} + 3 x^{2} + 1)^{4}} d x$ is equal to :
(where $C$ is a constant of integration)

\frac{x^{4}}{6 (2 x^{4} + 3 x^{2} + 1)^{3}} + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{x^{12}}{6 (2 x^{4} + 3 x^{2} + 1)^{3}} + C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{x^{4}}{(2 x^{4} + 3 x^{2} + 1)^{3}} + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{x^{12}}{(2 x^{4} + 3 x^{2} + 1)^{3}} + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{x^{12}}{6 (2 x^{4} + 3 x^{2} + 1)^{3}} + C$
$I = \int \frac{3 x^{13} + 2 x^{11}}{(2 x^{4} + 3 x^{2} + 1)^{4}} d x$

$= \int \frac{3 x^{13} + 2 x^{11}}{x^{16} {(2 + \frac{3}{x^{2}} + \frac{1}{x^{4}})}^{4}} d x$

$= \int \frac{(\frac{3}{x^{3}} + \frac{2}{x^{5}})}{{(2 + \frac{3}{x^{2}} + \frac{1}{x^{4}})}^{4}} d x$

Let $2 + \frac{3}{x^{2}} + \frac{1}{x^{4}} = t$
$\Rightarrow - (\frac{6}{x^{3}} + \frac{4}{x^{5}}) d x = d t$
$\Rightarrow (\frac{3}{x^{3}} + \frac{2}{x^{5}}) d x = - \frac{1}{2} d t$

$∴ I = - \frac{1}{2} \int \frac{1}{t^{4}} d t$
$= \frac{1}{6 t^{3}} + C$
$= \frac{x^{12}}{6 (2 x^{4} + 3 x^{2} + 1)^{3}} + C$

Suggest Corrections

Similar questions

Q. The inegral

\int \frac{3 x^{13} + 2 x^{11}}{(2 x^{4} + 3 x^{2} + 1)^{4}} d x

is equal to :
(where

C

is a constant of integration)

Q. The value of

\int \frac{3 x^{13} + 2 x^{11}}{(2 x^{4} + 3 x^{2} + 1)^{4}} d x

is equal to
(where

C

is constant of integration )

Q. The integral

\int \frac{3 x^{13} + 2 x^{11}}{(2 x^{4} + 3 x^{2} + 1)^{4}} d x

is equal to: (where C is a constant of integration)

Q. Find the derivative of

y = (x^{2} + 1) (x^{3} + 3)

Q. (2x⁴ + 3x² + 5)

\div

(x + 2)

Join BYJU'S Learning Program

The inegral ∫3x13+2x11(2x4+3x2+1)4dx is equal to : (where C is a constant of integration)

The correct option is B x126(2x4+3x2+1)3+CI=∫3x13+2x11(2x4+3x2+1)4 dx =∫3x13+2x11x16(2+3x2+1x4)4 dx =∫(3x3+2x5)(2+3x2+1x4)4 dx Let 2+3x2+1x4=t ⇒−(6x3+4x5)dx=dt ⇒(3x3+2x5)dx=−12 dt ∴ I=−12∫1t4 dt =16t3+C =x126(2x4+3x2+1)3+C

The inegral $\int \frac{3 x^{13} + 2 x^{11}}{(2 x^{4} + 3 x^{2} + 1)^{4}} d x$ is equal to :
(where $C$ is a constant of integration)