MCQ
Evaluate: $\int \frac{\sin x}{1+\sin x} d x$
- A$\sec x-\tan x+C$
- B$\sec x+\tan x+x+C$
- C$\sec x+\tan x+C$
- ✓$\sec x-\tan x+x+C$
✓
Answer
Correct option: D.
$\sec x-\tan x+x+C$
(d) : Let $I=\int \frac{\sin x}{1+\sin x} d x=\int \frac{\sin x(1-\sin x)}{(1+\sin x)(1-\sin x)} d x$
$=\int \frac{\sin x-\sin ^2 x}{\cos ^2 x} d x=\int \sec x \tan x d x-\int \tan ^2 x d x$
$=\int \sec x \tan x d x-\int\left(\sec ^2 x-1\right) d x=\sec x-\tan x+x+C$
$=\int \frac{\sin x-\sin ^2 x}{\cos ^2 x} d x=\int \sec x \tan x d x-\int \tan ^2 x d x$
$=\int \sec x \tan x d x-\int\left(\sec ^2 x-1\right) d x=\sec x-\tan x+x+C$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Let $\vec a, \vec b, \vec c$ three unit vectors such that $\mathop a\limits^ \to \mathop {.b}\limits^ \to + \mathop b\limits^ \to \mathop {.c}\limits^ \to - \mathop a\limits^ \to \mathop {.c}\limits^ \to = \frac{3}{2}$ Then the value of $\mathop a\limits^ \to \mathop {.b}\limits^ \to + \mathop b\limits^ \to \mathop {.c}\limits^ \to + \mathop c\limits^ \to \mathop {.a}\limits^ \to $
→The number of real solutions of $x^{7}+5 x^{3}+3 x+1=$ $0$ is equal to............
→Let $y = {t^{10}} + 1$ and $x = {t^8} + 1,$ then ${{{d^2}y} \over {d{x^2}}}$ is
→The feasible, region for an LPP is shown shaded in the figure. Let Z = 3x - 4y be the objective function. A minimum of Z occurs at:
If $f(x) = \left\{ \begin{array}{l}\,\,\,\,\,\,\,{e^x};\,\,\,\,x \le 0\\|1 - x|;\,\,x > 0\end{array} \right.$, then
→Which of the following is the integrating factor of $x d y / d x-y=x^4-3 x$ ?
→The function $f : A \rightarrow B$ defined by $f(x) = 4x + 7, x \in R$ is:
→If $\vec{a}$ and $\vec{b}$ are vectors in space given by $\vec{a}=\frac{\hat{i}-2 \hat{j}}{\sqrt{5}}$ and $\vec{b}=\frac{2 \hat{i}+\hat{j}+3 \hat{k}}{\sqrt{14}}$, then the value of $(2 \vec{a}+\vec{b}) \cdot[(\vec{a} \times \vec{b}) \times(\vec{a}-2 \vec{b})]$ is
→The angle between a line with direction ratios $2 : 2 : 1$ and a line joining $(3, 1, 4)$ to $(7, 2, 12)$ is
→If the determinant $\begin{vmatrix}\text{a}&\text{b}&2\text{a}\alpha+3\text{b}\\\text{b}&\text{c}&2\text{b}\alpha+3\text{c}\\2\text{a}\alpha+ 3\text{b}&2\text{b}\alpha+3\text{c}&0\end{vmatrix}=0,$ then:
→