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How do you integrate (x/(x+1)) dx without using substitution.

A tricky question which is actually really simple if you know the technique and will save a lot of time during the exam. The method is to simply add 1 and minus one to the numerator. so the integral becomes ...
Answered by • Maths tutor
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Differentiate 3x^(3) + 7x^(2) -4x

Using the formula for differentiation: if y=a x N then dy/dx= N a*x N-1 apply this to each term in the equation given; first term: dy/dx= 9x 2 second term: dy/dx= 14xthird term: dy/dx= - 4Combining all three...
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Answered by Michelle W. • Maths tutor
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Express (3-5x)/(x+3)^2 in the form A/(x+3) + B/(x+3)^2

A needs to be multiplied up by x+3 to make the fraction have the same in denominator as the other expressions. Then you need to equate the numerators. 3 - 5x = A(x+3) + B You can gain two simultaneous equati...
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The quadratic equation (k+1)x^2 + (5k - 3)x + 3k = 0 has equal roots. Find the possible values of k

We know the discriminant (b^2 - 4ac) must be equal to zero for an equation to have equal roots (think about the fact that the square root of this is taken in the quadratic equation). So we can form the equat...
MI
Answered by Molly I. • Maths tutor
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The graphs of functions f(x)=e^x and h(x)=e^(-.5x), where x is a real number and 0<x<1 ,lie on a plane. Draw these functions and find the area they and the line x=0.6 enclose using integration correct to 3 decimal places

∫ f(x)dx [.6, 0] - ∫ h(x)dx [.6,0]∫ f(x)dx = e^x....... f(x)dx [.6, 0] = (e^.6)-(e^0)=.822∫ h(x)dx = -2e^(-.5x)........... ∫ h(x)dx [.6,0]= (-2e^-.3)-(-2e^0)= .518.822 - .518= .304Therefore area enclosed = ....
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Answered by Brendan B. • Maths tutor
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