(D) माना $I = \int x \sqrt{\frac{2 \sin(x^2-1) - 2 \sin(x^2-1) \cos(x^2-1)}{2 \sin(x^2-1) + 2 \sin(x^2-1) \cos(x^2-1)}} dx$ $I = \int x \sqrt{\frac{2

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

${\log _e}\left| {\sec \left( {\frac{{{x^2} - 1}}{2}} \right)} \right| + c$

(D) माना $I = \int x \sqrt{\frac{2 \sin(x^2-1) - 2 \sin(x^2-1) \cos(x^2-1)}{2 \sin(x^2-1) + 2 \sin(x^2-1) \cos(x^2-1)}} dx$ $I = \int x \sqrt{\frac{2 \sin(x^2-1) [1 - \cos(x^2-1)]}{2 \sin(x^2-1) [1 + \cos(x^2-1)]}} dx$ $I = \int x \sqrt{\frac{2 \sin^2(\frac{x^2-1}{2})}{2 \cos^2(\frac{x^2-1}{2})}} dx$ $I = \int x \tan(\frac{x^2-1}{2}) dx$ माना $t = \frac{x^2-1}{2}$,तब $dt = x dx$ $I = \int \tan(t) dt = \ln|\sec(t)| + c$ $I = \ln|\sec(\frac{x^2-1}{2})| + c$

Class 12 Mathematics 7-1.Indefinite Integral Integration by substitution

Difficult

${x^2} \ne n\pi + 1, n \in N$ (प्राकृत संख्याओं का समुच्चय) के लिए,समाकलन $\int {x\sqrt {\frac{{2\sin \left( {{x^2} - 1} \right) - \sin 2\left( {{x^2} - 1} \right)}}{{2\sin \left( {{x^2} - 1} \right) + \sin 2\left( {{x^2} - 1} \right)}}} } dx$ क्या है?

JEE MAIN 2019 All JEE MAIN

A
${\log _e}\left| {\frac{1}{2}{{\sec }^2}\left( {{x^2} - 1} \right)} \right| + c$
B
$\frac{1}{2}{\log _e}\left| {\sec \left( {{x^2} - 1} \right)} \right| + c$
C
$\frac{1}{2}{\log _e}\left| {{{\sec }^2}\left( {\frac{{{x^2} - 1}}{2}} \right)} \right| + c$
D
${\log _e}\left| {\sec \left( {\frac{{{x^2} - 1}}{2}} \right)} \right| + c$