Find the Integral 4 square root of x

Problem

(∫_^)(4√(,x)*d(x))

Solution

1. Rewrite the radical expression using a fractional exponent to make it easier to integrate.

√(,x)=x(1/2)

2. Apply the constant multiple rule for integration by moving the constant outside the integral.

(∫_^)(4*x(1/2)*d(x))=4*(∫_^)(x(1/2)*d(x))

3. Use the power rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1) for n≠−1

4*(∫_^)(x(1/2)*d(x))=4⋅(x(1/2+1))/(1/2+1)+C

4. Simplify the exponent and the denominator.

4⋅(x(3/2))/(3/2)+C

5. Multiply by the reciprocal of the denominator to find the final coefficient.

4⋅2/3*x(3/2)+C

8/3*x(3/2)+C

Final Answer

(∫_^)(4√(,x)*d(x))=8/3*x(3/2)+C

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