What is the integral of (9xe^{x^2}+5/x-5^x+3x^2) ?

The integral of (9xe^{x^2}+5/x-5^x+3x^2) is 9/2 e^{x^2}+5ln|x|-(5^x)/(ln(5))+x^3+C

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integral of (9xe^{x^2}+5/x-5^x+3x^2)

\int (9 x e^{x^{2}} + \frac{5}{x} - 5^{x} + 3 x^{2}) d x

\frac{9}{2} e^{x^{2}} + 5 ln ∣ x ∣ - \frac{5 ^{x}}{ln ( 5 )} + x^{3} + C

Solution steps

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

\int 9 x e^{x^{2}} d x = \frac{9}{2} e^{x^{2}}

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int 5^{x} d x = \frac{5 ^{x}}{ln ( 5 )}

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

= \frac{9}{2} e^{x^{2}} + 5 ln ∣ x ∣ - \frac{5 ^{x}}{ln ( 5 )} + x^{3}

Add a constant to the solution

= \frac{9}{2} e^{x^{2}} + 5 ln ∣ x ∣ - \frac{5 ^{x}}{ln ( 5 )} + x^{3} + C

x \to - 2 lim (n (x))

\frac{2 x ^{3}}{5 y ^{3}}

\int \frac{1}{x x ^{2} - 100} d x

\frac{\partial}{\partial y} (e^{x y z^{7}} y z^{7})

\frac{d v}{d t} = k (250 - v)

What is the integral of (9xe^{x^2}+5/x-5^x+3x^2) ?
The integral of (9xe^{x^2}+5/x-5^x+3x^2) is 9/2 e^{x^2}+5ln|x|-(5^x)/(ln(5))+x^3+C