## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

${\int }_{0}^{\pi /2}ln\text{?}\left(1-{k}^{2}{sin}^{2}x\right)\frac{\text{d}x}{\sqrt{1-{k}^{2}{sin}^{2}x}}=ln\text{?}k\text{'}\text{?}\mathbf{K}\left(k\right)$

BI (323)(1)

2.

${\int }_{0}^{\pi /2}ln\left(1-{k}^{2}{sin}^{2}x\right)\frac{{sin}^{2}x\text{?}\text{d}x}{\sqrt{1-{k}^{2}{sin}^{2}x}}=\frac{1}{{k}^{2}}\left\{\left({k}^{2}-2+ln\text{?}k\text{'}\right)K\left(k\right)+\left(2-ln\text{?}k\text{'}\right)E\left(k\right)\right\}$

BI (323)(3)

3.12

${\int }_{0}^{\pi /2}ln\left(1-{k}^{2}{sin}^{2}x\right){cos}^{2}x\frac{\text{?}\text{d}x}{\sqrt{1-{k}^{2}{sin}^{2}x}}=\frac{1}{{k}^{2}}\left[\left(1+k{\text{'}}^{2}-k{\text{'}}^{2}ln\text{?}k\text{'}\right)K\left(k\right)-\left(2-ln\text{?}k\text{'}\right)E\left(k\right)\right]$

BI (323)(6)

4.

${{\int }^{\text{​}}}_{\pi /2}^{0}ln\left(1-{k}^{2}{sin}^{2}x\right)\frac{\text{?}\text{d}x}{\sqrt{{\left(1-{k}^{2}{sin}^{2}x\right)}^{3}}}=\frac{1}{k{\text{'}}^{2}}\left[\left({k}^{2}-2\right)K\left(k\right)-\left(2+ln\text{?}k\text{'}\right)E\left(k\right)\right]$

BI (323)(9)

5.12

${\int }_{0}^{\pi /2}ln\left(1-$

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required