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$={\displaystyle \int \left(se{c}^{2}x+secxtanx\right)dx}$

$={\displaystyle \int se{c}^{2}x.dx}+{\displaystyle \int secxtanxdx}$

$=tanx+secx+C$

$\begin{array}{l}={\displaystyle \int 2x^2}.dx–{\displaystyle \int 3sinx}.dx+{\displaystyle \int \mathrm{5\surd x}}dx\\ =\frac{2x^3}{3}+3cosx+\frac{5x^{3/2}}{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}+\; C\\ =\frac{2x^3}{3}+3cosx+\frac{10x^{3/2}}{3}+\; C\end{array}$

$={\displaystyle \int 2x}dx–{\displaystyle \int 3cosx}+e^{x}dx$

$\begin{array}{l}=\frac{2x^2}{2}-3sinx+e^x+\; C\\ =x^2-3sinx+e^x+C\end{array}$

National Law University Kochi follows the seat reservation policy as sanctioned by the government of India. The university offers a total of 136 seats for its students. However, the seats are unevenly reserved for students belonging to a special category. Among them, there are Scheduled Castes and Scheduled Tribes Categories. NLU offers 8 % for its SC students and 2% for its ST students. 

Yenepoya Institute of Technology offers decent placements annually to its BTech students. As per the official website, Yenepoya Institute of Technology achieved an 80% placement rate in the recent placement session. The branch-wise total offers made during Yenepoya Institute of Technology placements between 2023 and 2024 are presented below:

The last date for Nehru College of Management application form is not mentioned on the official website of the institute. However some important TANCET dates are as follows: 

• Registration starting January 24, 2025, with the last date to apply being February 28, 2025

Candidates are required to fill out the forms based on these application dates. 

$\begin{array}{l}\begin{array}{l}={\displaystyle \int \left(3x^2.x^{1/2}+2x.x^{1/2}+3x^{1/2}\right)}.dz\hfill \end{array}\end{array}$

$\begin{array}{l}\begin{array}{l}={\displaystyle \int \left(3x^{5/2}+2x^{3/2}+3x^{4/2}\right)}.dx\hfill \end{array}\end{array}$

$\begin{array}{l}\begin{array}{l}={\displaystyle \int 3x^{5/2}}.dx+{\displaystyle \int 2x^{3/2}}.dx+{\displaystyle \int 3x^{1/2}}.dx\hfill \end{array}\\ =3·\frac{x^{7/2}}{7/2}+\frac{2·x^{5/2}}{5/2}+\frac{3·x^{3/2}}{3/2}+\; C\\ =\frac{6·x^{7/2}}{7}+\frac{4x^{5/2}}{5}+\frac{6}{3}{x}^{3/2}+\; C\\ =\frac{6x^{7/2}}{7}+\frac{4·x^{5/2}}{5}+2x^{3/2}+\; C.\end{array}$

$\begin{array}{l}\int (\surd x-x·x^{1/2})dx\\ \int (\surd x-x^{3/2})·dx\\ \int x^{1/2}·dx-\int x^{3/2}·dx\\ \frac{x^{3/2}}{3/2}-\frac{x^{5/2}}{5/2}+C\\ \frac{2}{3}{x}^{3/2}-\frac{2}{5}{x}^{5/2}+\end{array}$ c

$\begin{array}{l}\int \frac{x^3-x^2}{x-1}+\frac{x-1}{x-1}dx\\ \int \left(x^2\frac{(x-1)}{x-1}+1\right)dx\\ \begin{array}{ll}={\displaystyle \int \left(x^2+1\right)}dx\hfill & \hfill \end{array}\end{array}$

$\begin{array}{l}\begin{array}{l}={\displaystyle \int x^2}.dx+{\displaystyle \int 1}.dx\hfill \end{array}\\ =\frac{x^3}{3}+x+\; C\end{array}$

Chennais Amirta International Institute of Hotel Management BSc is a three-year programme. The course structure includes six semesters. It is based on the Choice-based Credit System (CBCS). The curriculum includes various core and elective subjects, each carrying certain credits. Through the elective subjects, students can specialise in Food Production & Patisserie, Food & Beverage Services, Housekeeping, or Front Office. It also includes a project work during the fifth semester. In the last semester, students are required to undergo an internship (Industrial Practicum).

$\begin{array}{l}={\displaystyle \int \left(x^3.x^{–1/2}+3x.x^{–1/2}+4.x^{–1/2}\right)}dx\\ =\int \left(x^{5/2}+3x^{1/2}+4x^{-1/2}\right)dx\\ =\frac{x^{\frac{5}{2}+1}}{\frac{5}{2}+1}+3·\frac{x^{1/2+1}}{\frac{1}{2}+1}+4·\frac{x^{-1/2+1}}{-\frac{1}{2}+1}\\ =\frac{x^{7/2}}{7/2}+\frac{3·x^{3/2}}{3/2}+\frac{4x^{1/2}}{1/2}+C\\ =\frac{2}{7}{x}^{7/2}+2x^{3/2}+8x^{1/2}+C\\ =\frac{2}{7}{x}^{7/2}+2x^{3/2}+\mathrm{8\surd x}+C.\end{array}$

As per the National Law University Kochi admission guidelines, the eligibility criteria for BA LLB (Hons) requires candidates must have a 45% in their Higher Secondary School Examination (10+2) system or an equivalent examination. In the case of SC/ST/Person with Disability, 42% is also eligible. Therefore, candidates can get admission to NLU Kochi BA LLB (Hons) with 60& in Class 12th. 

Admission to the BA programme at Nazareth College of Arts and Science is strictly merit-based. Students are shortlisted based on their Class 12 performance, and no entrance exam is required. The college evaluates applications by reviewing academic records and publishes merit lists accordingly for final selection.

Nehru College of Management follows an online application process. Candidates are required to follow the steps given below to successfully complete the application process: 

Step 1: Visit the official website of the institute. 

Step 2: Fill out the google form present on the admissions section. 

Step 3: Complete the application process by ssubmitting the form with relevant details. 

After completing a BA from Nazareth College of Arts and Science, students can explore career paths in fields such as content writing, teaching, civil services, journalism, digital marketing, and public relations. They may also pursue higher studies like MA, MBA, or B.Ed. The college's skill-based curriculum helps enhance job readiness and industry exposure.

$\begin{array}{l}\int \left(\frac{x^3}{x^2}+\frac{5x^2}{x^2}-\frac{4}{x^2}\right)dx\\ \begin{array}{ll}={\displaystyle \int (x+5-4x^{–2})}dx\hfill & \hfill \end{array}\end{array}$

$\begin{array}{l}\begin{array}{l}={\displaystyle \int x}.dx+{\displaystyle \int 5}dx–{\displaystyle \int 4x^{–2}}dx\hfill \end{array}\\ =\frac{x^2}{2}+5x-4\frac{x^{-2+1}}{-2+1}\\ =\frac{x^2}{2}+5x-\frac{4x^{-1}}{-1}\\ =\frac{x^2}{2}+5x+\frac{4}{x}+\; C\end{array}$

Nazareth College of Arts and Science has a diverse range of recruiters participating in its placement drives. Some key names include Larsen & Toubro Infotech, TCS BPS, Infosys BPO, Sundaram Finance, Tech Mahindra, Sutherland Global Services, Star Health Insurance, Mphasis, CAMS Outsourcing, and Qspiders. These recruiters highlight the college's strong industry connections and career support for BA students.