Evaluate the following indefinite integral.
{eq}\displaystyle \int \bigg(\dfrac {x} {\sqrt {1 - x^4}}\bigg)\ dx {/eq}
Question:
Evaluate the following indefinite integral.
{eq}\displaystyle \int \bigg(\dfrac {x} {\sqrt {1 - x^4}}\bigg)\ dx {/eq}
Indefinite Integration:
Indefinite integration is the process of determining the anti-derivative of a function. After the integration, we add a constant term to the final expression which is known as integral constant. There are various methods to determine the integral of a function like substitution method, method of partial fractions, and the method of by parts. Some of the important formulas of integrals are:
{eq}\int \sin^{-1} (x) \ dx= \dfrac{1}{\sqrt{1-x^2}} + C \\ \int x^n \ dx = \dfrac{x^{n+1}}{n+1} + C {/eq}
Answer and Explanation: 1
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View this answerGiven:
{eq}\int \bigg(\dfrac {x} {\sqrt {1 - x^4}}\bigg)\ dx {/eq}
Rewriting the above expression as:
{eq}\int \bigg(\dfrac {x} {\sqrt {1 -...
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Chapter 12 / Lesson 11Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.