What is the integral of ((3-7x+9x^2e^{7x})/(x^2)) ?

The integral of ((3-7x+9x^2e^{7x})/(x^2)) is -3/x-7ln|x|+9/7 e^{7x}+C

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integral of ((3-7x+9x^2e^{7x})/(x^2))

\int (\frac{3 - 7 x + 9 x ^{2} e ^{7 x}}{x ^{2}}) d x

- \frac{3}{x} - 7 ln ∣ x ∣ + \frac{9}{7} e^{7 x} + C

Solution steps

\int \frac{3 - 7 x + 9 x ^{2} e ^{7 x}}{x ^{2}} d x

Expand

\frac{3 - 7 x + 9 x ^{2} e ^{7 x}}{x ^{2}} : \frac{3}{x ^{2}} - \frac{7}{x} + 9 e^{7 x}

= \int \frac{3}{x ^{2}} - \frac{7}{x} + 9 e^{7 x} 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 \frac{3}{x ^{2}} d x - \int \frac{7}{x} d x + \int 9 e^{7 x} d x

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

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int 9 e^{7 x} d x = \frac{9}{7} e^{7 x}

= - \frac{3}{x} - 7 ln ∣ x ∣ + \frac{9}{7} e^{7 x}

Add a constant to the solution

= - \frac{3}{x} - 7 ln ∣ x ∣ + \frac{9}{7} e^{7 x} + C

\int_{0}^{5} 100 - 10 t d t

f (x) = - \frac{761}{12} x^{4} + \frac{2089}{3} x^{3} - \frac{31015}{12} x^{2} + \frac{11432}{3} x - 1833, at x = 5.35

\int \frac{5 x ^{2} - 3 x + 18}{9 x - x ^{3}} d x

\frac{d}{d x} (e^{a x} + arctan (c x))

y = \frac{7}{3 x ^{4}}

What is the integral of ((3-7x+9x^2e^{7x})/(x^2)) ?
The integral of ((3-7x+9x^2e^{7x})/(x^2)) is -3/x-7ln|x|+9/7 e^{7x}+C