Integrals

11 flashcards · Mathematics · by Athena Papkouf

1. ∫x−1dx\int x^{-1} d x∫x−1dx

   ln⁡(x)\ln (x)ln(x)

2. ∫∣x∣dx\int|x| d x∫∣x∣dx

   xx22\frac{x \sqrt{x^{2}}}{2}2xx2 ​​

3. ∫sin⁡(x)dx\int \sin (x) d x∫sin(x)dx

   −cos⁡(x)-\cos (x)−cos(x)

4. ∫cos⁡(x)dx\int \cos (x) d x∫cos(x)dx

   sin⁡(x)\sin (x)sin(x)

5. ∫xadx\int x^{a} d x∫xadx

   xa+1a+1,a≠−1\frac{x^{a+1}}{a+1}, \quad a \neq-1a+1xa+1​,a̸​=−1

6. ∫1sin⁡2(x)dx\int \frac{1}{\sin ^{2}(x)} d x∫sin2(x)1​dx

   −cot⁡(x)-\cot (x)−cot(x)

7. ∫1cos⁡2(x)dx\int \frac{1}{\cos ^{2}(x)} d x∫cos2(x)1​dx

   tan⁡(x)\tan (x)tan(x)

8. ∫1x2+1dx\int \frac{1}{x^{2}+1} d x∫x2+11​dx

   arctan⁡(x)\arctan (x)arctan(x)

9. ∫−1x2+1dx\int \frac{-1}{x^{2}+1} d x∫x2+1−1​dx

   arccot⁡(x)\operatorname{arccot}(x)arccot(x)

10. ∫11−x2dx\int \frac{1}{\sqrt{1-x^{2}}} d x∫1−x2 ​1​dx

    arcsin⁡(x)\arcsin (x)arcsin(x)

11. ∫−11−x2dx\int \frac{-1}{\sqrt{1-x^{2}}} d x∫1−x2 ​−1​dx

    arccos⁡(x)\arccos (x)arccos(x)