Question

⎰((56x^6+4x^3-2x^5)dx) can be written as ax^p+bx^q+cx^r+c

Answer 1

\[\int 56x^6+4x^3-2x^5\,\mathrm dx\]

use the sum rule
\[=56\int x^6\,\mathrm dx+4\int x^3\,\mathrm dx-2\int x^5\,\mathrm dx\]

then the power rule
\[\boxed{\displaystyle\int x^n\,\mathrm dx=\frac1nx^{n+1}+\color{gray}c}\]

\[=\]

Answer 2

combine all the constant of integration, in to a single constant


then set your answer equal to \[ax^p+bx^q+cx^r+c\]

hence, by direct comparison , solve for \(a,p,b,q,r\) and \(c\)