Question

find the indefinite integral as indicated.
int \frac { d } { d x } left( x ^ { 7 } + 6 x ^ { 3 } + 9
ight) d x
int \frac { d } { d x } left( x ^ { 7 } + 6 x ^ { 3 } + 9
ight) d x =

Explanation:

Step1: Use the fundamental theorem of calculus

The fundamental theorem of calculus states that if \(F(x)\) is an antiderivative of \(f(x)\), then \(\int f(x)dx=F(x)+C\). Also, \(\int\frac{d}{dx}(g(x))dx = g(x)+C\)

Step2: Apply the formula

Here \(g(x)=x^{7}+6x^{3}+9\). So \(\int\frac{d}{dx}(x^{7}+6x^{3}+9)dx=x^{7}+6x^{3}+9 + C\)

Answer:

\(x^{7}+6x^{3}+9 + C\)