What is the integral of (2+7x)/(1+x^2) ?

The integral of (2+7x)/(1+x^2) is 2arctan(x)+7/2 ln|1+x^2|+C

Popular >

integral of (2+7x)/(1+x^2)

\int \frac{2 + 7 x}{1 + x ^{2}} d x

2 arctan (x) + \frac{7}{2} ln 1 + x^{2} + C

Solution steps

\int \frac{2 + 7 x}{1 + x ^{2}} d x

Expand

\frac{2 + 7 x}{1 + x ^{2}} : \frac{2}{1 + x ^{2}} + \frac{7 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{2}{1 + x ^{2}} d x + \int \frac{7 x}{1 + x ^{2}} d x

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

\int \frac{7 x}{1 + x ^{2}} d x = \frac{7}{2} ln 1 + x^{2}

= 2 arctan (x) + \frac{7}{2} ln 1 + x^{2}

Add a constant to the solution

= 2 arctan (x) + \frac{7}{2} ln 1 + x^{2} + C

\int_{0}^{\frac{π}{2}} 9 cos^{2} (x) d x

\int e^{x} 4 - e^{x} d x

6 - x, x, 1

\frac{d}{d x} (\frac{8 x}{7 - cot ( x )})

x ln (x), - x + 1, [1, 3]

What is the integral of (2+7x)/(1+x^2) ?
The integral of (2+7x)/(1+x^2) is 2arctan(x)+7/2 ln|1+x^2|+C