What is the integral of 2x^6-3x^5+11x^2+1 ?

The integral of 2x^6-3x^5+11x^2+1 is (2x^7)/7-(x^6)/2+(11x^3)/3+x+C

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integral of 2x^6-3x^5+11x^2+1

\int 2 x^{6} - 3 x^{5} + 11 x^{2} + 1 d x

\frac{2 x ^{7}}{7} - \frac{x ^{6}}{2} + \frac{11 x ^{3}}{3} + x + C

Solution steps

\int 2 x^{6} - 3 x^{5} + 11 x^{2} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x^{6} d x - \int 3 x^{5} d x + \int 11 x^{2} d x + \int 1 d x

\int 2 x^{6} d x = \frac{2 x ^{7}}{7}

\int 3 x^{5} d x = \frac{x ^{6}}{2}

\int 11 x^{2} d x = \frac{11 x ^{3}}{3}

\int 1 d x = x

= \frac{2 x ^{7}}{7} - \frac{x ^{6}}{2} + \frac{11 x ^{3}}{3} + x

Add a constant to the solution

= \frac{2 x ^{7}}{7} - \frac{x ^{6}}{2} + \frac{11 x ^{3}}{3} + x + C

\int (- g t + V) d t

\int e^{9 x} cos (5 x) d x

y = - x^{3} + 2 x

sin (\frac{π}{6} + x)

\frac{d}{d x} (1 - e^{- 4 x})

What is the integral of 2x^6-3x^5+11x^2+1 ?
The integral of 2x^6-3x^5+11x^2+1 is (2x^7)/7-(x^6)/2+(11x^3)/3+x+C