What is the general form of an antiderivative for \( f(x) = 3x^{2} \)?

Evaluate the integrals i) \( \int_{2}^{4} \int_{0}^{x} \int_{0}^{x+y} z d x d y d x \)

A function \( f \) is defined as \( f(x)=\frac{5}{(x+2)^{2}}-\frac{2}{x+2} \) for \( x>0 \). Find an expression for \( f^{\prime}(x) \) and determine whether \( f \) is an increasing function, a decreasing function or aeither.

Найдите неопределенный интеграл: \( \, \int (3x^2 + 2x - 1) \, dx \)

\( z \int _ { 0 } ^ { + \infty } t ^ { z } e ^ { - t } d t \)

\( y ^ { \prime \prime } - ( \lambda _ { 1 } + \lambda _ { 2 } ) y ^ { \prime } + \lambda _ { 1 } \lambda _ { 2 } y = 0 , y = C _ { 1 } e ^ { \lambda _ { 1 } x } + C _ { 2 } e ^ { \lambda _ { 2 } x } \)