Write a value of 1+ x+ dx - Vidyadip

Question

Write a value of $\int\frac{1+\cot\text{x}}{\text{x}+\log\sin\text{x}}\text{ dx}$

✓

Answer

Let $\text{I}=\int\frac{1+\cot\text{x}}{\text{x}+\log\sin\text{x}}\text{ dx}$
Let $\text{x}+\log\sin\text{x}=\text{t}$
$(1+\cot\text{x})\text{dx}=\text{dt}$
$\therefore\ \text{I}=\int\frac{\text{dt}}{\text{t}}$
$=\log|\text{t}|+\text{C}$
Hence,
$\text{I}=\log|\text{x}+\log\sin\text{x}|+\text{C}$

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 "3 Marks Question" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

For each of the differential equations in find the general solution:
$\text{x}^5\frac{\text{dy}}{\text{dx}}=-\text{y}^5$

Solve system of linear equations, using matrix method.

2x + 3y + 3z = 5

x - 2y + z = -4

3x - y - 2z = 3

Test whether the following relations $R_3$ are:

Reflexive.
Symmetric.
Transitive.

$R_3$ on $R$ defined by $(\text{a, b})\in\text{R}_3\Leftrightarrow\ \text{a}^2-4\text{ab}+3\text{b}^2=0$

Find $\frac{\text{dy}}{\text{dx}}$ in the following cases:
$\tan^{-1}\big(\text{x}^2+\text{y}^2\big)=\text{a}$

Evaluate the following integrals:
$\int\limits^{2\pi}_0\cos^{-1}(\cos\text{x})\text{dx}$

Find $\frac{\text{dy}}{\text{dx}},\ \text{if y}=12(1-\cos \text{t}),\ \text{x}=10(\text{t}-\sin\text{t}),\ -\frac{\pi}{2}<\text{t}<\frac{\pi}{2}$

Let f be a function defined on [a, b] such that f′(x) > 0, for all $\text{x}\in(\text{a},\text{b}).$ Then prove that f is an increasing function on (a, b).

A ladder, 5 metre long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides down wards at the rate of 10cm/ sec, then find the rate at which the angle between the floor and ladder is decreasing when lower end of ladder is 2 metres from the wall.

Evaluate the following integrals:
$\int^\limits3_{-3}|\text{x}+1|\text{dx}$

If a vector$\vec{\text{a}}$ is perpendicular to two non-collinear vectors $\vec{\text{b}}$ and $\vec{\text{c}},$ then show that $\vec{\text{a}}$ is perpendicular to every vector in the plane of $\vec{\text{b}}$ and $\vec{\text{c}}.$