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

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Integrating Other Functions (Trig, ln & e etc)
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What is ∫cos⁡(x) dx\int \cos(x) \, dx?

sin⁡(x)+C\sin(x) + C

What is ∫sec⁡2(x) dx\int \sec^2(x) \, dx?

tan⁡(x)+C\tan(x) + C

What is ∫e5x dx\int e^{5x} \, dx?

15e5x+C\frac{1}{5}e^{5x} + C

What is ∫ln⁡(x) dx\int \ln(x) \, dx?

xln⁡(x)−x+Cx\ln(x) - x + C

What is ∫11+x2 dx\int \frac{1}{1 + x^2} \, dx?

arctan⁡(x)+C\arctan(x) + C

What is ∫11−x2 dx\int \frac{1}{\sqrt{1 - x^2}} \, dx?

arcsin⁡(x)+C\arcsin(x) + C

What is ∫sin⁡(3x) dx\int \sin(3x) \, dx?

−13cos⁡(3x)+C-\frac{1}{3}\cos(3x) + C

What is ∫sec⁡(x)tan⁡(x) dx\int \sec(x)\tan(x) \, dx?

sec⁡(x)+C\sec(x) + C

Using the identity sin⁡2(x)=1−cos⁡(2x)2\sin^2(x) = \frac{1 - \cos(2x)}{2}, what is ∫sin⁡2(x) dx\int \sin^2(x) \, dx?

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

What is ∫e7x−3 dx\int e^{7x-3} \, dx?

17e7x−3+C\frac{1}{7}e^{7x-3} + C

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