Common integrals table

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Elementary

Trigonometric

• $$\int\text{sin}(x)\mathrm{d}x\eq \cos(x)\plusc{}$$
• $$\int\cos(x)\mathrm{d}x\eq \sin(x)\plusc{}$$

Basic Trigonometric

• $$\int\cos^2(x)\mathrm{d}x\eq \frac{\sin(2x)+2x}{4}\plusc{}\eq\frac{\sin(x)\cos(x)+x}{2}\plusc{}$$
• $$\int\sin^2(x)\mathrm{d}x$$ $$\eq \frac{2x-\sin(2x)}{4}\plusc{}\eq x-\frac{x-\sin(x)\cos(x)}{2}\plusc{}$$
• $$\int\tan^2(x)\mathrm{d}x$$ ???

Involving: $$\big(\sqrt{1\pm x^2}\ \big)^{\pm 1}$$

• $$\int\Big(\sqrt{1-x^2}\Big)\mathrm{d}x$$ $$\eq\frac{x\sqrt{1-x^2} + \arcsin(x)}{2} \plusc$$