Question

What is the value of x to the power n log x integration?

Answer 1

Answer:

Step-by-step explanation:

∫xⁿlogx dx  =  ∫logx.xⁿ dx

= logx ∫ xⁿdx  −  ∫ (d/dx(logx) . ∫ xⁿdx) dx

[Integrating by parts by taking logx as the first function and xⁿ as the second]

= logx . xⁿ⁺¹/n+1 − ∫ ( 1/x . xⁿ⁺¹/n+1)dx

= xⁿ⁺¹ . logx/n+1 - 1/n+1 ∫ xⁿ dx

= 1/n+1[ xⁿ⁺¹ . logx] - 1/n+1 * xⁿ⁺¹/n+1 + C

= xⁿ⁺¹ . logx/n+1  -  xⁿ⁺¹/(n+1)² + C