Find the following integral: $\int \frac{2-3 \sin x}{\cos ^{2} x} d x$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) Given integral: $\int \frac{2-3 \sin x}{\cos ^{2} x} d x$
Split the fraction into two parts:
$= \int \left( \frac{2}{\cos ^{2} x} - \frac{3 \sin x}{\cos ^{2} x} \right) d x$
Using trigonometric identities $\frac{1}{\cos ^{2} x} = \sec ^{2} x$ and $\frac{\sin x}{\cos ^{2} x} = \tan x \sec x$:
$= \int 2 \sec ^{2} x \, d x - 3 \int \tan x \sec x \, d x$
Integrating the terms:
$= 2 \tan x - 3 \sec x + C$
where $C$ is an arbitrary constant.

Explore More

Similar Questions

$\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d x$ is

$\int \sin^{-1}(\cos x) \, dx = $

$\int \sqrt{1+x^{2}} \, dx$ is equal to

$\int \frac{1}{\log_x e} \, dx = $

Find an anti-derivative (or integral) of the function $\sin 2x - 4e^{3x}$ by the method of inspection.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo