MyQuestionIcon

1

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

Binomial Coefficients

Evaluate ∫7 x...

Question

Evaluate $\int \frac{(7 x + 2)}{7 x^{2} + 4 x + 5} d x$
(where $C$ is constant of integration)

A

\frac{1}{2} ln ∣ ∣ 7 x^{2} + 4 x + 5 ∣ ∣ + C

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

B

- \frac{1}{2} ln ∣ ∣ 7 x^{2} + 4 x + 5 ∣ ∣ + C

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

C

\frac{1}{2} ln ∣ ∣ 7 x^{2} - 4 x + 5 ∣ ∣ + C

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

D

- \frac{1}{2} ln ∣ ∣ 7 x^{2} - 4 x + 5 ∣ ∣ + C

.

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

Open in App

Solution

The correct option is A $\frac{1}{2} ln ∣ ∣ 7 x^{2} + 4 x + 5 ∣ ∣ + C$
Let $I = \int \frac{(7 x + 2)}{7 x^{2} + 4 x + 5} d x$
Put $7 x^{2} + 4 x + 5 = t \Rightarrow 2 (7 x + 2) d x = d t$
$\Rightarrow I = \frac{1}{2} \int \frac{d t}{t} = \frac{1}{2} ln | t | + C$

$\Rightarrow I = \frac{1}{2} ln ∣ ∣ 7 x^{2} + 4 x + 5 ∣ ∣ + C$ .

Suggest Corrections

thumbs-up

0

Similar questions

\int \frac{d x}{(5 x - 2) (2 x + 7)}

C

is constant of integration)

\int \frac{7 x + 2}{\sqrt{2 x^{2} + 5 x}} d x

C

is constant of integration)

\int \frac{x^{7} d x}{{(1 - x^{2})}^{5}}

C

is constant of integration)

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

C

is constant of integration)

\int \frac{3 x^{2} + 7}{x^{8} + 3 x^{3} + 5 x} d x

C

is constant of integration)

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Binomial Coefficients

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon