Evaluate the Integral

Problem

(∫_^)(4*x3*sin(x4)*d(x))

Solution

1. Identify the inner function for substitution, which is u=x4

2. Differentiate u with respect to x to find d(u)=4*x3*d(x)

3. Substitute u and d(u) into the original integral.

(∫_^)(sin(u)*d(u))

4. Integrate the sine function with respect to u

−cos(u)+C

5. Substitute back the original expression for u to get the final result in terms of x

−cos(x4)+C

Final Answer

(∫_^)(4*x3*sin(x4)*d(x))=−cos(x4)+C

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