Solving an indefinite integral involves using integration techniques, such as u-substitution or integration by parts, to simplify the integrand to a known function. After simplifying, the integral can be solved using the power rule or other integration rules.
The power rule states that the integral of x^n is equal to (x^(n+1))/(n+1) + C, where C is a constant. This rule can be applied to solve indefinite integrals of polynomial functions.
To apply u-substitution, choose a part of the integrand to substitute with u, such that du/dx can be easily found. Substitute u and du into the integral, and then solve for u in terms of x. Finally, substitute back in the original variable and simplify the integral.
Yes, integration by parts can be used to solve this integral. This technique involves choosing two parts of the integrand, u and dv, such that the product of du/dx and v can be easily integrated or differentiated. The integral can then be solved using the formula ∫u dv = uv - ∫v du.
Yes, there are several general strategies for solving indefinite integrals, such as u-substitution, integration by parts, and trigonometric substitution. However, the best strategy to use depends on the specific integrand and requires practice and familiarity with integration techniques.