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integrate the following: 2x^4 - 4/sqrt(x) +3 with respect to x

The 3 terms of this equation can be integrated separately. The general integration of xⁿ is (xⁿ⁺¹)/n+1 where n is a real number not equal to -1. This can be applied to the terms 2x

Answered by Adrien F. • Maths tutor

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Why is the derivative of the exponential function itself?

The exponential function is defined as a power series, which we may (for reasons that are beyond the scope of A-level) differentiate term by term to get another power series. The general term of the serie...

Answered by George B. • Maths tutor

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evaluate the integral of lnx

this is an example of an integration by parts problem, we must use integration by parts to evaluate this integral;although this would not be entirely obvious as the integral does not seem to be the produc...

Answered by Aaron R. • Maths tutor

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dy/dx= 2x/2 - 1/4x, what is d2y/dx2?

(2x)/2= 2x^-2d2y/dx2= -4x^-1 - 1/4

Answered by Gloria N. • Maths tutor

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Find ∫(2x^5 -4x^-3 +5) dx

So we have to integrate these 3 terms one by one. To integrate 2x⁵ you add 1 to the power of x, so that becomes 6, you then divide the coefficient by the new power of x. So 3/6=1/2 giving the i...

Answered by Peter S. • Maths tutor

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