6.5 Contents

1. $\int\sin^n(a·x)\thinspace dx$ 🔧

2. $\int\cos^n(a·x)\thinspace dx$ 🔧

3. $\int\csc^n(a·x)\thinspace dx$ 🔧

4. $\int\sec^n(a·x)\thinspace dx$ 🔧

5. $\int\tan^n(a·x)\thinspace dx$ 🔧

6. $\int\cot^n(a·x)\thinspace dx$ 🔧

7. $\int\sec^n(a·x)·\tan(a·x)\thinspace dx$ 🔧

8. $\int\csc^n(a·x)·\cot(a·x)\thinspace dx$ 🔧

9. $\int 1/(1\pm sin(a·x))\thinspace dx$ 🔧

1. $\int 1/(1\pm cos(a·x))\thinspace dx$ 🔧

2. $\int\sin(a·x)·\sin(b·x)\thinspace dx$ 🔧

3. $\int\sin(a·x)·\cos(b·x)\thinspace dx$ 🔧

4. $\int\cos(a·x)·\cos(b·x)\thinspace dx$ 🔧

5. $\int\sin^m(a·x)·\cos^n(b·x)\thinspace dx$ (sine reduction) 🔧

6. $\int\sin^m(a·x)·\cos^n(b·x)\thinspace dx$ (cosine reduction) 🔧

6.4.1 $\int\sin^n(a·x)\thinspace dx$ 🔧

$$\int\sin^n(a·x)\thinspace dx=$$

Proof

Example

$$\int\sin^3(a·x)\thinspace dx$$

6.4.2 $\int\cos^n(a·x)\thinspace dx$ 🔧

$$\int\cos^n(a·x)\thinspace dx=$$

Proof

Example

$$\int\cos^3(a·x)\thinspace dx$$

6.4.3 $\int\csc^n(a·x)\thinspace dx$ 🔧

$$\int\csc^n(a·x)\thinspace dx=$$

Proof

Example

$$\int\csc^3(a·x)\thinspace dx$$

6.4.4 $\int\sec^n(a·x)\thinspace dx$ 🔧

$$\int\sec^n(a·x)\thinspace dx=$$

Proof

Example

$$\int\sec^3(a·x)\thinspace dx$$

6.4.5 $\int\tan^n(a·x)\thinspace dx$ 🔧

$$\int\tan^n(a·x)\thinspace dx=$$

Proof

Example

$$\int\tan^3(a·x)\thinspace dx$$

6.4.6 $\int\cot^n(a·x)\thinspace dx$ 🔧

$$\int\cot^n(a·x)\thinspace dx=$$

Proof

Example

$$\int\cot^3(a·x)\thinspace dx$$

6.4.7 $\int\sec^n(a·x)·\tan(a·x)\thinspace dx$ 🔧

Proof

6.4.8 $\int\csc^n(a·x)·\cot(a·x)\thinspace dx$ 🔧

Proof

6.4.9 $\int 1/(1\pm sin(a·x))\thinspace dx$ 🔧

Proof

6.4.A $\int 1/(1\pm cos(a·x))\thinspace dx$ 🔧

Proof

6.4.B $\int\sin(a·x)·\sin(b·x)\thinspace dx$ 🔧

Proof

6.4.C $\int\sin(a·x)·\cos(b·x)\thinspace dx$ 🔧

Proof

6.4.D $\int\cos(a·x)·\cos(b·x)\thinspace dx$ 🔧

Proof

6.4.E $\sin^m(a·x)·\cos^n(b·x)$ (sine reduction) 🔧

Proof

6.4.F $\sin^m(a·x)·\cos^n(b·x)$ (cosine reduction) 🔧

Proof