Evaluate the Integral integral of 3x^5 with respect to x

Problem

(∫_^)(3*x5*d(x))

Solution

1. Identify the constant and the power of x in the integrand. The constant is 3 and the exponent is n=5

2. Apply the constant multiple rule for integration, which allows the constant 3 to be moved outside the integral.

(∫_^)(3*x5*d(x))=3*(∫_^)(x5*d(x))

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

3*(∫_^)(x5*d(x))=3⋅(x(5+1))/(5+1)+C

4. Simplify the expression by adding the exponents and dividing by the new power.

3⋅(x6)/6+C

5. Reduce the fraction by dividing the numerator and denominator by their greatest common factor, 3

1/2*x6+C

Final Answer

(∫_^)(3*x5*d(x))=1/2*x6+C

Want more problems? Check here!