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

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

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

Answer

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)