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How do I know when to integrate using by parts or by substitution?

When integrating a function which can be defined as a combination of two functions, it can be difficult to tell whether or not to use by parts. We can spot when to use by parts if we look at the composite fu...
EK
Answered by Eesa K. • Maths tutor
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Using a suitable substitution, or otherwise, find the integral of [x/((7+2*(x^2))^2)].

The point of using a substitution when dealing with integrals is to reduce the problem from a very complicated integral to a simplistic one. How can we achieve this with our integral? Well, we know that when...
GF
Answered by George F. • Maths tutor
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The polynomial f(x) is defined by f(x) = 18x^3 + 3x^2 + 28x + 12. Use the Factor Theorem to show that (3x+2) is a factor of f(x).

The factor theorem states that if (x+a) is a factor of f(x), then f(-a)=0. This basically means that if (x+a) is a factor of f(x), then when (x+a)=0, f(x)=0, i.e. when x=-a, f(-a)=0. Our (x+a) in this case i...
GF
Answered by George F. • Maths tutor
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Use simultaneous equations to find the points where the following lines cross: 3x - y = 4 and x^2 + 7y = 5

The points where the lines cross are the points where the two equations equal each other. To do this we solve simultaneous equations. Call equations as follows:(a) 3x - y = 4(b) x 2 + 7y = 5 First take (a) a...
EM
Answered by Emma M. • Maths tutor
3783 Views

Differentiate 4(x^3) + 3x + 2 with respect to x

Solution: 12x 2 + 3 Working: General differentiation formular: d/dx (ax n ) = an(x n-1 ) So we multiply the coefficient (constant infront) of the x term by the power of x (in this case: n) and reduce the pow...
TD
Answered by Tutor77028 D. • Maths tutor
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