Integrating Other Functions (Trig, ln & e etc) (Edexcel A-Level Mathematics): Flashcards

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Integrating Other Functions (Trig, ln & e etc)
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What is the integral of sin⁡(x)\sin(x)?

−cos⁡(x)+C-\cos(x) + C

What is the integral of cos⁡(x)\cos(x)?

sin⁡(x)+C\sin(x) + C

How to integrate sec⁡2(x)\sec^2(x)?

tan⁡(x)+C\tan(x) + C

What is the integral of exe^x?

ex+Ce^x + C

Integrate ln⁡(x)\ln(x). What is the result?

xln⁡(x)−x+Cx \ln(x) - x + C

What is the integral of arcsin⁡(x)\arcsin(x)?

x⋅arcsin⁡(x)+1−x2+Cx \cdot \arcsin(x) + \sqrt{1-x^2} + C

How to integrate ekxe^{kx}?

1kekx+C\frac{1}{k}e^{kx} + C

What is the integral of sec⁡(x)tan⁡(x)\sec(x)\tan(x)?

sec⁡(x)+C\sec(x) + C

What is the integral of sin⁡2(x)\sin^2(x)?

x2−14sin⁡(2x)+C\frac{x}{2} - \frac{1}{4}\sin(2x) + C

Integrate sec⁡2(3x)\sec^2(3x). What's the answer?

13tan⁡(3x)+C\frac{1}{3}\tan(3x) + C

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