Evalute the following integrals: 2 2x+ ^2x 2x+ -5 dx - Vidyadip

Question

Evalute the following integrals:
$\int\frac{2\cos2\text{x}+\sec^2\text{x}}{\sin2\text{x}+\tan\text{x}-5}\text{dx}$

✓

Answer

Let $\text{I}=\int\frac{2\cos2\text{x}+\sec^2\text{x}}{\sin2\text{x}+\tan\text{x}-5}\text{dx}$
Putting $\sin2\text{x}+\tan\text{x}-5=\text{t}$
$\Rightarrow2\cos2\text{x}+\sec^2\text{x}=\frac{\text{dt}}{\text{dx}}$
$\Rightarrow(2\cos2\text{x}+\sec^2\text{x})\text{dx}=\text{dt}$
$\therefore\text{I}=\int\frac{1}{\text{t}}\text{dt}$
$=\text{ln}|\text{t}|+\text{C}$
$=\text{ln}|\sin2\text{x}+\tan\text{x}-5|+\text{C} $ $\big[\because\text{t}=\sin2\text{x}+\tan\text{x}-5\big]$

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 "Solve the Following Question.(3 Marks)" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Form the differential equation of:all circles which pass through the origin and whose centres lie on X-axis.

Integrate the following functions w.r.t x:

$3^{\cos ^2 x} \sin 2 x$

Solve the following differential equations:

$\frac{d y}{d x}+y \cdot \sec x=\tan x$

Represent the following families of curves by forming the corresponding differential equation:
$\text{x}^2+(\text{y}-\text{b})^2=1$

Evaluate the following :

$\int \sqrt{\frac{9+x}{9-x}} \cdot d x$

Write the minors and cofactors of element of the first column of the following matrices and hence evaluate the determinant in case:
$\text{A}=\begin{vmatrix}-1&4\\2&3 \end{vmatrix}$

In $\Delta A B C$, if $a \cos A=b \cos B$ then prove that the triangle is either a right angled or an isosceles triangle.

Integrate the following functions w. r. t. x

$\int \frac{1}{3+2 \sin x} \cdot d x$

The volume of the spherical ball is increasing at the rate of $4 \pi \mathrm{cc} / \mathrm{sec}$. Find the rate at which the radius and the surface area are changing when the volume is $288 \pi \mathrm{cc}$.

Find the Cartesian form of the equation of the plane $\bar{r}=(\hat{i}+\hat{j})+s(\hat{i}-\hat{j}+2 \hat{k})+t(\hat{i}+2 \hat{j}+\hat{k})$