What is the integral from 0 to 1 of (2x+3)/(x^2+1) ?

The integral from 0 to 1 of (2x+3)/(x^2+1) is ln(2)+(3pi)/4

Popular >

integral from 0 to 1 of (2x+3)/(x^2+1)

\int_{0}^{1} \frac{2 x + 3}{x ^{2} + 1} d x

ln (2) + \frac{3 π}{4}

Decimal

3.04934 \dots

Solution steps

\int_{0}^{1} \frac{2 x + 3}{x ^{2} + 1} d x

Expand

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

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

\int_{0}^{1} \frac{3}{x ^{2} + 1} d x = \frac{3 π}{4}

= ln (2) + \frac{3 π}{4}

\int_{0}^{10} 0 d x

\int_{0}^{1} (9 x^{e} + 4 e^{x}) d x

\int_{0}^{8} 2 x - (x - 4) d x

\int_{0}^{8} x^{2} - 6 x + 8 d x

\int_{e}^{e^{2}} (\frac{1}{x ln ( x )}) d x

What is the integral from 0 to 1 of (2x+3)/(x^2+1) ?
The integral from 0 to 1 of (2x+3)/(x^2+1) is ln(2)+(3pi)/4