Question
Evaluate $\int \frac{\cos ^2 x}{1+\sin x} d x$
✓
Answer
Let
$I=\int \frac{\cos ^2 x}{1+\sin x} d x$
$I=\int \frac{1-\sin ^2 x}{1+\sin x} d x=\int \frac{(1-\sin x)(1+\sin x)}{1+\sin x} d x$
$I=\int(1-\sin x) d x=x+\cos x+\text { C }$
$I=\int \frac{\cos ^2 x}{1+\sin x} d x$
$I=\int \frac{1-\sin ^2 x}{1+\sin x} d x=\int \frac{(1-\sin x)(1+\sin x)}{1+\sin x} d x$
$I=\int(1-\sin x) d x=x+\cos x+\text { C }$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A family has two children. What is the probability that both the children are boys given that at least one of them is a boy?
Consider two points P and Q with position vectors $\vec{OP}=3 \vec{a}-2 \vec{b}$ and $\vec{OQ}=\vec{a}+\vec{b}$.
Find the position vector (externally) of a point R which divides the line joining P and Q in the ratio 2 : 1.
→Find the position vector (externally) of a point R which divides the line joining P and Q in the ratio 2 : 1.
Find the integral: $\int \frac{d x}{x^{2}-6 x+13}$
→In the figure which are the Collinear but not equal vectors?
Find intervals in which the function given by $f(x) = \frac{3}{{10}}{x^4} - \frac{4}{5}{x^3} - 3{x^2} + \frac{{36}}{5}x + 11$ is increasing or decreasing.
→Integrate the function $\frac{1}{x^{2}\left(x^{4}+1\right)^{\frac{3}{4}}}$
→Find the interval in which the function
$f(x) = x^2 + 2x – 5$
is strictly increasing or decreasing.
→$f(x) = x^2 + 2x – 5$
is strictly increasing or decreasing.
Write the degree of the following differrntial equation $\text{x} \Big(\frac{\text{dy}}{\text{dx}}\Big)^{3}+\text{y}\Big(\frac{\text{dy}}{\text{dx}}\Big)^{4}+\text{x}^{3}=0.$
→Classify the following as scalar and vector quantities.
Force.
Force.
On which of the following intervals is the function $f$ given by $f(x) = x^{100} + sinx – 1$, decreasing?
→