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How do you integrate (2x)/(1+x^2) with respect to x?

The key here is to recognise that this is in the form f'(x)/f(x). We can use the idea that integration is the inverse of differentiation, and the knowledge that the derivative of ln(f(x)) is equal to f'(x)/f...
Answered by • Maths tutor
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How do I derive Kepler's 3rd law using Newton's Law of gravitation, in the case of a circular orbit?

Kepler's 3rd law states that the cube of the radius, r from a planet is directly proportional to the square of the orbital period around it, T: r 3 ∝ T 2 (this is the result we want!) We know Newton's Law of...
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Answered by Greta C. • Physics tutor
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How do I know which is the null hypothesis, and which is the alternative hypothesis?

Generally, the null hypothesis is the one we want to reject, and the alternative is the one we want to prove is true. For example, if we were testing whether growing in the Sun made a plant grow healthier, w...
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Answered by Tegan C. • Maths tutor
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Differentiate the following: y=(7x^2+2)sinx

Differentiate using the product rule.Product rule: for y=uv , where u and v are functions of x, dy/dx=vdu/dx + udv/dxy=(7x 2 +2)sinx so u=(7x 2 +2) and v=sinx . By differentiating these functions:du/dx=14x a...
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Answered by Eleanor T. • Maths tutor
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Before leaving Les’s house, Neil swallowed some tablets which he found in the bathroom. Subsequently, back in his own flat, he set fire to the carpet (which belonged to the landlord) under the delusion that he was making a camp-fire. The fire spread rapid

It is likely that Neil may be charged with Unlawful Act Manslaughter. The case of Goodfellow derives a four-part test to test whether a person is guilty. This is; whether the defendant has committed an unlaw...
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Answered by Oliver A. • Law tutor
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