Evaluate: 5x + 3 x^ 2 +4x + 10 . - Vidyadip

Question

Evaluate: $\int\frac{\text{5x + 3}}{\sqrt{\text{x}^{2}+\text{4x + 10}}}$.

✓

Answer

$\text{I}=\int\frac{\text{5x + 3}}{\sqrt{\text{x}^{2}+\text{4x + 10}}}\text{dx}=\int\frac{\frac{5}{2}\text{(2x + 4)}-7}{\sqrt{\text{x}^{2}+\text{4x}+10}}$$=\frac{5}{2} \int\frac{\text{2x + 4}}{\sqrt{\text{x}^{2}+\text{4x + 10}}}\text{dx}-7 \int\frac{1}{\sqrt{\text{(x+2)}^{2}+(\sqrt{6})^{2}}}\text{dx}$
$ =5\cdot\sqrt{\text{x}^{2}+\text{4x + 10}}-7\log|\text{(x + 2)}+\sqrt{\text{x}^{2}+\text{4x}+10}|+\text{c}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from INTEGRALS→INTEGRALS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the area of the region lying in the first quadrant and bounded by $y = 4x^2, x = 0, y = 1$ and $y = 4.$

Write the following in the simplest form:
$\tan^{-1}\Big\{\frac{\sqrt{1+\text{x}^2}-1}{\text{x}}\Big\},\text{x}\neq0$

Evaluvate the following intregals:
$\int\frac{1}{1-\tan\text{x}}\text{ dx}$

Divide $64$ into two parts such that the sum of the cubes of two parts is minimum.

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is $\text{y}+2(\text{x}+1)=2\text{e}^{2\text{x}}.$

Evaluate the following integrals:
$\int\frac{1}{\sin\text{x}(3+2\cos\text{x})}\ \text{dx}$

A manufacturer has employed 5 skilled men and 10 semi-skilled men and makes two models A and B of an article. The making of one item of model A requires 2 hours work by a skilled man and 2 hours work by a semi-skilled man. One item of model B requires 1 hour by a skilled man and 3 hours by a semi-skilled man. No man is expected to work more than 8 hours per day. The manufacturer’s profit on an item of model A is Rs. 15 and on an item of model B is Rs. 10. How many of items of each model should be made per day in order to maximize daily profit? Formulate the above LPP and solve it graphically and find the maximum profit.

Evaluate the following:
$\tan\frac{1}{2}\Big(\cos^{-1}\frac{\sqrt5}{3}\Big)$

Let N denote the set of all natural numbers and R be the relation on$\text{N} \times \text{N}$defined by $\text{(a, b) R (c, d)}$ if ad$\text{(b + c) = bc(a + d)}$. Show that R is an equivalence relation.

$\text{Find}:\int \frac{\sin \theta\ \text{d}\theta}{(4 + \cos^{2} \theta) (2- \sin^{2} \theta)} \text{d} \theta$