What is the integral of (3+5x)/(1+x^2) ?

The integral of (3+5x)/(1+x^2) is 3arctan(x)+5/2 ln|1+x^2|+C

Popular >

integral of (3+5x)/(1+x^2)

\int \frac{3 + 5 x}{1 + x ^{2}} d x

3 arctan (x) + \frac{5}{2} ln 1 + x^{2} + C

Solution steps

\int \frac{3 + 5 x}{1 + x ^{2}} d x

Expand

\frac{3 + 5 x}{1 + x ^{2}} : \frac{3}{1 + x ^{2}} + \frac{5 x}{1 + x ^{2}}

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

\int \frac{3}{1 + x ^{2}} d x = 3 arctan (x)

\int \frac{5 x}{1 + x ^{2}} d x = \frac{5}{2} ln 1 + x^{2}

= 3 arctan (x) + \frac{5}{2} ln 1 + x^{2}

Add a constant to the solution

= 3 arctan (x) + \frac{5}{2} ln 1 + x^{2} + C

\int sin^{12} (x) cos (x) d x

x \to 0 lim ((1 + 5 x)^{\frac{2}{x}})

\frac{d y}{d x} = k_{1} (y - c_{1})

cos (X)

\frac{h ( x )}{x}

What is the integral of (3+5x)/(1+x^2) ?
The integral of (3+5x)/(1+x^2) is 3arctan(x)+5/2 ln|1+x^2|+C