What is the integral of (7x^2)ex^3+1 ?

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

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integral of (7x^2)ex^3+1

\int (7 x^{2}) e x^{3} + 1 d x

\frac{7 e x ^{6}}{6} + x + C

Solution steps

\int 7 x^{2} e x^{3} + 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 7 x^{2} e x^{3} d x + \int 1 d x

\int 7 x^{2} e x^{3} d x = \frac{7 e x ^{6}}{6}

\int 1 d x = x

= \frac{7 e x ^{6}}{6} + x

Add a constant to the solution

= \frac{7 e x ^{6}}{6} + x + C

f (x) = - 4 sin (4 x)

t an g e n t y = x + \frac{6}{x}, (3, 5)

81 y^{^{''}} + 180 y^{^{'}} + 125 y = 0, y (3) = 6, y^{^{'}} (3) = 6

\frac{d}{d x} (8 cos^{2} (x))

a re a 2 x^{3} - 6 x^{2} - 2 x + 6, - x^{3} + 3 x^{2} + x - 3

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