What is the integral of 1/(1+x^2)-e^x+5/x+1 ?

The integral of 1/(1+x^2)-e^x+5/x+1 is arctan(x)-e^x+5ln|x|+x+C

Popular >

integral of 1/(1+x^2)-e^x+5/x+1

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

arctan (x) - e^{x} + 5 ln ∣ x ∣ + x + C

Solution steps

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

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

\int e^{x} d x = e^{x}

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int 1 d x = x

= arctan (x) - e^{x} + 5 ln ∣ x ∣ + x

Add a constant to the solution

= arctan (x) - e^{x} + 5 ln ∣ x ∣ + x + C

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

\int \frac{x y}{x ^{2} + y ^{2}} d y

\int 6 sin^{6} (x) cos (x) d x

\int 12 x + 6 d x

\int cos^{2} (m x) d x

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