CameraIcon

SearchIcon

MyQuestionIcon

1

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

Property 1

Evaluate: ∫...

Question

Evaluate: $\int (4 x + 2) \sqrt[3]{x^{2} + x + 1 d x}$

Open in App

Solution

$I = \int (4 x + 2) \sqrt[3]{x^{2} + x + 1} d x$

let $x^{2} + x + 1 = t$
$\Rightarrow (2 x + 1) d x = d t$

$\Rightarrow I = 2 \int (2 x + 1) \sqrt[3]{x^{2} + x + 1} = \int t^{1 / 3} d t$

$= 2. \frac{t^{1 / 3 + 1}}{1 / 3 + 1} + c = 2 \times \frac{t^{4 / 3}}{4 / 3} + c = \frac{3}{2} {(x^{2} + x + 1)}^{4 / 3} + c$

Suggest Corrections

thumbs-up

0

Similar questions

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

\int \frac{2 x + 3}{\sqrt{x^{2} + 4 x + 1}} d x

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

Q. Evaluate the integral

\int \frac{2 x + 3}{\sqrt{x^{2} + 4 x + 1}} d x

\int \frac{2 x - 3}{\sqrt{x^{2} + x + 1}} d x

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Property 1

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon