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Integrate exp(2x)cos(8x) by parts

Let u=exp(2x) and v'=cos(8x)From these you can obtain u' and vu=2exp(2x) and v=1/8 sin(8x)Formula: integral(uv'dx)=uv-integral(vu'dx)=1/8 exp(2x)sin(8x)-integral(1/4 sin(8x)exp(2x))=1/8exp(2x)sin(8x)+1/16cos...
CD
Answered by Chloe D. • Maths tutor
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Solve the equation 8x^6 + 7x^3 -1 = 0

The first thing to recognise is this is a quadratic in disguise, therefore we can rewrite the equation in terms of a new variable y. Where y=x 3 The equation then becomes 8y 2 +7y-1=0 . We then factorise thi...
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Answered by Kelan P. • Maths tutor
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What is the best way to do well in my Italian GCSE oral exam?

Firstly, make sure you are aware of the topics your exam board uses in speaking exams, e.g. 'school', 'holidays' or 'hobbies' and commit to learning some key vocab for each topic. For example, if you're aske...
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Answered by Violetta K. • Italian tutor
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Integrate sinxcosx dx

Since the question is a trigonometry question, we shall use integration by recognisation, in which case, we found out that the derivative of sin x is cos x.Therefore by chain rule, we can integrate the funct...
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Answered by Harris L. • Maths tutor
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To what extent were Gorbachev's reforms responsible for the fall of the Soviet Union?

To blame Gorbachev alone is an oversimplification. Reforms may have accelerated the decline of the USSR, but their failure was contingent on long standing economic conditions. Firstly - what were Gorbachev's...
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Answered by Charlotte E. • History tutor
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