Question

Need done in less than 3 hours! Does anyone know this. Step by step please and thank you!!

Answer 1

`(9x^(10/3))/(5)- (26x^(9/2))/(9)+C`

Explanation:

Evaluate the given integral.

`\int\big(6x^(7/3)-13x^(7/2)\big) \ dx`

`\hrulefill`

Using the power rule.

`\boxed{\left\begin{array}{ccc}\text{\underline{The Power Rule for Integration:}}\\\\ \int x^n \ dx=(x^(n+1))/(n+1) \end{array}\right}`

`\int\big(6x^(7/3)-13x^(7/2)\big) \ dx\\\\\\\Longrightarrow (6x^(7/3+1))/(7/3+1)- (13x^(7/2+1))/(7/2+1)\\\\\\\Longrightarrow (6x^(10/3))/(10/3)- (13x^(9/2))/(9/2)\\\\\\\Longrightarrow ((3)6x^(10/3))/(10)- ((2)13x^(9/2))/(9)\\\\\\\Longrightarrow (18x^(10/3))/(10)- (26x^(9/2))/(9)\\\\\\\therefore \boxed{\boxed{ =(9x^(10/3))/(5)- (26x^(9/2))/(9)+C}}`

Thus, the problem is solved.