Find the indefinite integral.

{eq}\displaystyle \int 5x^4 sin(x^5) \; dx {/eq}


Find the indefinite integral.

{eq}\displaystyle \int 5x^4 sin(x^5) \; dx {/eq}


We will use the substitution method to make the problem simpler and easy to evaluate here the integral will be converted into a simpler form and then after solving we will add the integration constant.

Answer and Explanation: 1

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To solve the integral we will use the substitution method:

{eq}\int 5x^{4}\sin (x^{5})dx {/eq}

Now let us put:

{eq}x^{5}=t\\ 5x^{4}dx=dt {/eq}


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Evaluating Definite Integrals Using the Fundamental Theorem


Chapter 16 / Lesson 2

In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.

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