_ ^ ( 2 + 2x 1 + 2x ) , , e^x dx =

MCQ

$\int_{}^{} {\left( {\frac{{2 + \sin 2x}}{{1 + \cos 2x}}} \right)\,\,{e^x}dx = } $

A
${e^x}\cot x + c$
B
$ - {e^x}\cot x + c$
C
$ - {e^x}\tan x + c$
✓
${e^x}\tan x + c$

✓

Answer

Correct option: D.

${e^x}\tan x + c$

d
(d)$\int_{}^{} {\left( {\frac{{2 + \sin 2x}}{{1 + \cos 2x}}} \right){\rm{ }}{e^x}\,dx} = \int_{}^{} {\left( {\frac{{2{e^x}}}{{1 + \cos 2x}}} \right)dx} + \int_{}^{} {\frac{{{e^x}\sin 2x}}{{1 + \cos 2x}}dx} $
$ = \int_{}^{} {{e^x}{{\sec }^2}x\,dx} + \int_{}^{} {{e^x}\tan x\,dx = {e^x}\tan x + 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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The co-ordinates of points $A,B,C,D$ are $(a, 2, 1), (1, -1, 1), (2, -3, 4)$ and $(a+1, a+2, a+3)$ respectively. If $AB = 5$ and $CD = 6$, then $a = $

→

Which of the following is true?

* defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on Z.
* defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on Q.
All binary commutative operations are associative.
Subtraction is a binary operation on N.

→

$\cot ^{-1} \frac{\sqrt{1-x^2}}{x}$ equal to :

→

Number of positive solution of the equation,$\int\limits_0^x {\,\,{{\left( {t\,\, - \,\,\left\{ t \right\}} \right)}^2}}$ $dt = 2 (x - 1)$ where $\{ \}$ denotes the fractional part function is :

→

The area enclosed by the closed curve $C$ given by the differential equation $\frac{d y}{d x}+\frac{x+a}{y-2}=0, y(1)=0$ is $4 \pi$.

Let $P$ and $Q$ be the points of intersection of the curve $C$ and the $y$-axis. If normals at $P$ and $Q$ on the curve $C$ intersect $x$-axis at points $R$ and $S$ respectively, then the length of the line segment $RS$ is

→

The points $O,\,A,\,B,\,C,\,D$ are such that $\overrightarrow {OA} = a,$ $\overrightarrow {OB} = b,\,$ $\overrightarrow {OC} = 2a + 3b$ and $\overrightarrow {OD} = a - 2b.$ If $|a|\, = 3\,|b|,$ then the angle between $\overrightarrow {BD} $ and $\overrightarrow {AC} $ is

→

If $A=\left[\begin{array}{lll}2 & -3 & 4\end{array}\right], B=\left[\begin{array}{l}3 \\ 2 \\ 2\end{array}\right], X=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]$ and $Y=\left[\begin{array}{l}2 \\ 3 \\ 4\end{array}\right]$, then $A B+X Y$ equals

→

If $A$ and $B$ are $3 × 3$ matrices and $| A | \ne 0$, then which of the following are true?

→

If $|\vec{\text{a}}|=\big|\vec{\text{b}}\big|,$ then $\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big)=$