Evaluate: 2x+2 ^2x ^2x dx - Vidyadip

Question

Evaluate:
$\int\frac{\cos2\text{x}+2\sin^2\text{x}}{\sin^2\text{x}}\text{dx}$

✓

Answer

$\int\Big(\frac{\cos2\text{x}+2\sin^2\text{x}}{\sin^2\text{x}}\Big)\text{dx}$
$=\int\Big(\frac{1-2\sin^2\text{x}+2\sin^2\text{x}}{\sin^2\text{x}}\Big)\text{dx}$ $[\because\cos2\text{x}=1-2\sin^2\text{x}]$
$=\int\text{cosec}^2\text{x}\text{ dx}$
$=-\cot\text{x}+\text{c}$

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 "2 Marks" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let A = {1, 2, 3, 4} and B = {a, b} be two sets. Write the total number of onto functions from A to B.

If $\text A = \begin{bmatrix}\frac{2}{3}&1&\frac{5}{3}\\ \frac{1}{3}&\frac{2}{3}&\frac{4}{3}\\ \frac{7}{3}&2&\frac{2}{3}\end{bmatrix} \text{and}\ \text{B} = \begin{bmatrix}\frac{2}{5}&\frac{3}{5}&1\\ \frac{1}{5}&\frac{2}{5}&\frac{4}{5}\\ \frac{7}{5}&\frac{6}{5}&\frac{2}{3}\end{bmatrix}, $ then compute 3A - 5B.

If $\begin{bmatrix}\text{xy}&4\\\text{z}+6&\text{x}+\text{y} \end{bmatrix}=\begin{bmatrix}8&\text{w}\\0&6 \end{bmatrix},$ write the value of (x + y + z).

Integrate the following integrals:
$\int\sin\text{mx}\cos\text{nx dx m}\neq\text{n}$

If $\text{P(A)}=0.3,\text{P(B)}=0.6,\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=0.5,$ find $\text{P}(\text{A}\cup\text{B}).$

What is the principal value of $\cos^{-1}\Big(\cos\frac{2\pi}{3}\Big)+\sin^{-1}\Big(\sin\frac{2\pi}{3}\Big)$

Solve:
$4\sin^{-1}\text{x}={\pi}-\cos^{-1}\text{x}$

Find the Cartesian equation of the following plane:

$\vec{\text{r}}.\Big(2\hat{\text{i}}+3\hat{\text{j}}-4\hat{\text{k}}\Big)=1$

If $\vec{\text{a}}=\hat{\text{i}}-\hat{\text{j}}$ and $\vec{\text{b}}=-\hat{\text{j}}+2\hat{\text{k}},$ find $\big(\vec{\text{a}}-2\vec{\text{b}}\big).\big(\vec{\text{a}}+\vec{\text{b}}\big).$

Find the domain of the following function:

$\text{f(x)}=\sin^{-1}\text{x}+\sin^{-1}2\text{x}$