What is the integral from 0 to 1 of (2x+1)/(x^2+1) ?

The integral from 0 to 1 of (2x+1)/(x^2+1) is ln(2)+pi/4

Popular >

integral from 0 to 1 of (2x+1)/(x^2+1)

\int_{0}^{1} \frac{2 x + 1}{x ^{2} + 1} d x

ln (2) + \frac{π}{4}

Decimal

1.47854 \dots

Solution steps

\int_{0}^{1} \frac{2 x + 1}{x ^{2} + 1} d x

Expand

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} \frac{2 x}{x ^{2} + 1} d x + \int_{0}^{1} \frac{1}{x ^{2} + 1} d x

\int_{0}^{1} \frac{2 x}{x ^{2} + 1} d x = ln (2)

\int_{0}^{1} \frac{1}{x ^{2} + 1} d x = \frac{π}{4}

= ln (2) + \frac{π}{4}

\int_{2}^{5} \frac{k}{x ^{3}} d x

\int_{0}^{2} (x - x^{2}) d x

\int_{0}^{2 x^{2}} t ln (t) d t

\int_{1}^{8} 3 x - 1 d x

\int_{1}^{8} 1 + x^{3} d x

What is the integral from 0 to 1 of (2x+1)/(x^2+1) ?
The integral from 0 to 1 of (2x+1)/(x^2+1) is ln(2)+pi/4