2x-1 2x+1 dx= - Vidyadip

MCQ

$\int\frac{\cos2\text{x}-1}{\cos2\text{x}+1}\text{ dx}=$

A
$\tan\text{x}-\text{x}+\text{C}$
B
$\text{x}+\tan\text{x}+\text{C}$
✓
$\text{x}-\tan\text{x}+\text{C}$
D
$-\text{x}-\cot\text{x}+\text{C}$

✓

Answer

Correct option: C.

$\text{x}-\tan\text{x}+\text{C}$

$\text{I}=\int\frac{\cos2\text{x}-1}{\cos2\text{x}+1}\text{ dx}$
$\text{I}=-\int\frac{1-\cos2\text{x}}{1+\cos2\text{x}}\text{ dx}$
$\text{I}=-\int\frac{2\sin^2\text{x}}{2\cos^2\frac{\text{x}}{2}}\text{ dx}$
$\text{I}=-\int\tan^2\text{x dx}$
$\text{I}=-\int(\sec^2\text{x}-1)\text{dx}$
$\text{I}=-(\tan\text{x}-\text{x})+\text{C}$
$\text{I}=\text{x}-\tan\text{x}+\text{C}$

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 "M.C.Q (1 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 $O$ be the origin and the position vector of $A$ and $B$ be $2 \hat{i}+2 \hat{j}+\hat{k}$ and $2 \hat{i}+4 \hat{j}+4 \hat{k}$ respectively. If the internal bisector of $\angle A O B$ meets the line $A B$ at $\mathrm{C}$, then the length of $\mathrm{OC}$ is

$\int {\frac{{dx}}{{5 + 4\cos x}}} $ $= \lambda\, \tan^{-1}$ $\left( {m\tan \frac{x}{2}} \right)$ $+ C$ then :

If the angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{3}$ and $|\vec{a} \times \vec{b}|=3 \sqrt{3}$, then the value of $\vec{a} \cdot \vec{b}$ is

For every integer $n$, let $a_n$ and $b_n$ be real numbers. Let function $f: I R \rightarrow$ $IR$ be given by $f(x)=\left\{\begin{array}{ll}a_n+\sin \pi x, & \text { for } x \in[2 n, 2 n+1] \\ b_n+\cos \pi x, & \text { for } x \in(2 n-1,2 n)\end{array}\right.$, for all integers $n$.

If $f$ is continuous, then which of the following hold$(s)$ for all $n$ ?

$(A)$ $a_{n-1}-b_{n-1}=0$ $(B)$ $a_n-b_n=1$ $(C)$ $a_n-b_{n+1}=1$ $(D)$ $a_{n-1}-b_n=-1$

The projections of a line segment on x, y and z axes are 12, 4 and 3 respectively. The length and direction cosines of the line segment are:

If $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$ are unit vectors such that $ (\vec{a} \times \vec{b}) \cdot(\vec{c} \times \vec{d})=1 $ $ \text { and } \vec{a} \cdot \vec{c}=\frac{1}{2},$ then

If $\text{f(x)}=\text{x}^2+\frac{\text{x}^2}{1+\text{x}^2}+\frac{\text{x}^2}{(1+\text{x}^2)}+....+\frac{\text{x}^2}{(1+\text{x}^2)}+....,$ then at $x = 0, f(x) :$

The value of $\hat{\text{i}}.\big(\hat{\text{j}}\times\hat{\text{k}}\big)+\hat{\text{j}}.\big(\hat{\text{i}}\times\hat{\text{k}}\big)+\hat{\text{k}}.\big(\hat{\text{i}}\times\hat{\text{j}}\big),$ is:

Solve:$\sin { \left( { \tan }^{ -1 }\text{x} \right) } ,\left| \text{x} \right| <1$ is equal to:

If the matrix $A=\left[\begin{array}{cc}3-2 x & x+1 \\ 2 & 4\end{array}\right]$ is singular then $x =?$