CameraIcon

SearchIcon

MyQuestionIcon

1

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

Sum of Coefficients of All Terms

Evaluate: ∫...

Question

Evaluate: $\int x \frac{d}{d x} (12 x^{3} + 4 x + 5) d x$

A

36 x^{4} + 4 x^{2} + c

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

B

9 x^{3} + 4 x^{2} + c

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

C

9 x^{4} + 2 x^{2} + c

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

D

9 x^{3} + 2 x^{2} + c

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

Open in App

Solution

The correct option is B $9 x^{4} + 2 x^{2} + c$
let,

$I = \int x \frac{d}{d x} (12 x^{3} + 4 x + 5) d x$

$u \frac{d v}{d x} = \frac{d u v}{d x} - \frac{v d u}{d x} u = x x \frac{d v}{d x} = \frac{d x v}{d x} - v ∴ \int x \frac{d v}{d x} = \int \frac{d x v}{d x} - v d x \int x \frac{d v}{d x} = x v - \int v d x + k v = 12 x^{3} + 4 x + 5 I = \int x \frac{d}{d x} (12 x^{3} + 4 x + 5) d x = 12 x^{4} + 4 x^{2} + 5 x - \int (12 x^{3} + 4 x + 5) d x + k I = 12 x^{4} + 4 x^{2} + 5 x - [3 x^{4} + 2 x^{2} + 5 x] + C I = 9 x^{4} + 2 x^{2} + C$

Suggest Corrections

thumbs-up

0

Similar questions

\int \frac{x^{2} + 9}{x^{4} - 2 x^{2} + 81} d x

\int \frac{4 x + 3}{2 x^{2} + 2 x + 5} d x

- 4 x^{2} + {(2 x^{2} - 3) - (4 - 3 x^{2})}

{lim}_{x \to \sqrt{2}} \frac{x^{9} - {3 x}^{8} + x^{6} - {9 x}^{4} - {4 x}^{2} - 16 x + 84}{x^{5} - {3 x}^{4} - 4 x + 12}

Q. The degree of the polynomial
5

x^{4}

x^{3}

x^{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Sum of Coefficients of All Terms

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Sum of Coefficients of All Terms

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon