6.4.1 $\int\sin(x)\thinspace dx$ 🔧
$$\int\sin(x)\thinspace dx=-\cos(x)+C$$
Proof
6.4.2 $\int\cos(x)\thinspace dx$ 🔧
$$\int\cos(x)\thinspace dx=\sin(x)+C$$
Proof
6.4.3 $\int\sec(x)\thinspace dx$ 🔧
$$\int\sec(x)\thinspace dx=\ln\big(|\sec(x)+\tan(x)|\big)+C$$
Proof
6.4.4 $\int\csc(x)\thinspace dx$ 🔧
$$\int\csc(x)\thinspace dx=-\ln\big(|\csc(x)+\cot(x)|\big)+C$$
Proof
6.4.5 $\int\tan(x)\thinspace dx$ 🔧
$$\int\tan(x)\thinspace dx=\ln\big(|\sec(x)|\big)+C$$
Proof
6.4.6 $\int\cot(x)\thinspace dx$ 🔧
$$\int\cot(x)\thinspace dx=\ln\big(|\sin(x)|\big)+C$$
Proof
6.4.7 $\int\sin^2(x)\thinspace dx$ 🔧
$$\int\sin^2(x)\thinspace dx=\frac{x}{2}-\frac{\sin(2\cdot x)}{4}+C$$
Proof
6.4.8 $\int\cos^2(x)\thinspace dx$ 🔧
$$\int\cos^2(x)\thinspace dx=\frac{x}{2}+\frac{\sin(2\cdot x)}{4}+C$$
Proof
6.4.9 $\int\sec^2(x)\thinspace dx$ 🔧
$$\int\sec^2(x)\thinspace dx=\tan(x)+C$$
Proof
6.4.A $\int\csc^2(x)\thinspace dx$ 🔧
$$\int\csc^2(x)\thinspace dx=-\cot(x)+C$$
Proof
6.4.B $\int\tan^2(x)\thinspace dx$ 🔧
$$\int\tan^2(x)\thinspace dx=\tan(x)-x+C$$
Proof
6.4.C $\int\cot^2(x)\thinspace dx$ 🔧
$$\int\cot^2(x)\thinspace dx=-\cot(x)-x+C$$
Proof
6.4.D $\int\sin^{-1}(x)\thinspace dx$ 🔧
$$\int\sin^{-1}(x)\thinspace dx=x\cdot\sin^{-1}(x)+\sqrt{1-x^2}+C$$
Proof
6.4.E $\int\cos^{-1}(x)\thinspace dx$ 🔧
$$\int\cos^{-1}(x)\thinspace dx=x\cdot\cos^{-1}(x)-\sqrt{1-x^2}+C$$
Proof
6.4.F $\int\sec^{-1}(x)\thinspace dx$ 🔧
$$\int\sec^{-1}(x)\thinspace dx=x\cdot\sec^{-1}(x)-\ln\big|x+\sqrt{x^2-1}\big|+C$$
Proof
6.4.G $\int\csc^{-1}(x)\thinspace dx$ 🔧
$$\int\csc^{-1}(x)\thinspace dx=x\cdot\csc^{-1}(x)+\ln\big|x+\sqrt{x^2-1}\big|+C$$
Proof
6.4.H $\int\tan^{-1}(x)\thinspace dx$ 🔧
$$\int\tan^{-1}(x)\thinspace dx=x\cdot\tan^{-1}(x)-\frac{1}{2}\cdot\ln|x^2+1|+C$$
Proof
6.4.I $\int\cot^{-1}(x)\thinspace dx$ 🔧
$$\int\cot^{-1}(x)\thinspace dx=x\cdot\cot^{-1}(x)+\frac{1}{2}\cdot\ln|x^2+1|+C$$
Proof
