What is the integral of (3e^{5x}-7/x+4/(1+x^2)) ?

The integral of (3e^{5x}-7/x+4/(1+x^2)) is 3/5 e^{5x}-7ln|x|+4arctan(x)+C

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integral of (3e^{5x}-7/x+4/(1+x^2))

\int (3 e^{5 x} - \frac{7}{x} + \frac{4}{1 + x ^{2}}) d x

\frac{3}{5} e^{5 x} - 7 ln ∣ x ∣ + 4 arctan (x) + C

Solution steps

\int 3 e^{5 x} - \frac{7}{x} + \frac{4}{1 + 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 3 e^{5 x} d x - \int \frac{7}{x} d x + \int \frac{4}{1 + x ^{2}} d x

\int 3 e^{5 x} d x = \frac{3}{5} e^{5 x}

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int \frac{4}{1 + x ^{2}} d x = 4 arctan (x)

= \frac{3}{5} e^{5 x} - 7 ln ∣ x ∣ + 4 arctan (x)

Add a constant to the solution

= \frac{3}{5} e^{5 x} - 7 ln ∣ x ∣ + 4 arctan (x) + C

\frac{d}{d x} (tan (x^{2} - 1))

\int 2 x y z^{3} d y

\frac{d y}{d x} = 15 - 3 y

x \to 0 lim (\frac{sin ^{6} ( x )}{x})

\frac{\partial}{\partial y} (x^{2} sin^{2} (y))

What is the integral of (3e^{5x}-7/x+4/(1+x^2)) ?
The integral of (3e^{5x}-7/x+4/(1+x^2)) is 3/5 e^{5x}-7ln|x|+4arctan(x)+C