x2(x3 + 1) is the best you can do there.
For it to be a definite integral, you would need to specify a range. We can however give you the indefinite integral. The easiest way to do this is to think of it not as a fraction, but as a negative exponent: 1/x2 = x-2 It then becomes quite easy to integrate, as we can say in general: ∫(axn) dx = ax(n + 1) / (n + 1) + C In this case then, we have: ∫(x-2) dx = -x-1 + C, or -1/x + C
x2 + 7x + 6 = (x + 6) (x + 1)
3x2 + 2x + 3 + x2 + x + 1 = 4x 2+ 3x + 4
square root of (x2 + 1) = no simplification (square root of x2) + 1 = x + 1
Int sqrt(1+x2)/x = sqrt(1+x2) + LN [(sqrt(1+x2) - x -1) / (sqrt(1+x2) - x +1)]
The integral of -x2 is -1/3 x3 .
x2 + x2 + x2 = (1 + 1 + 1)x2 = 3x2
Hopefully I did this one correctly, if anyone sees an error please correct it. This is the problem:∫(2x+7)/(x2+2x+5)I rewrote the integral as:2∫x/(x2+2x+5) + 7∫1/(x2+2x+5)Both of these parts of the integral is in a form that should be listed in most integral tables in a calculus text book or on-line. From these tables the integral is the following:2*[(1/2)ln|x2+2x+5| - (1/2)tan-1((2x+2)/4)] + 7*[(1/2)tan-1((2x+2)/4)]Combining like terms gives the following:ln|x2+2x+5| + (5/2)*tan-1((2x+2)/4)
for the integral of (2x)dx/(1+x2 ) Take (1+x2 ) as your 'u' substitution. find du, du= 2x dx use u substitution to write new integral, integral of du/u the integral of du/u= ln abs(u) + C therefore, your original problem becomes an answer with ln ln abs (1+x2) + C *abs refers to absolute value of the parentheses
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The integral of a single term of a polynomial, in the form of AxN is (A/N+1) x (N+1). The first integral of 2x is x2 + C. The second integral of 2x is the first integral of x2 + C, which is 1/3x3 + Cx + C.
The integral of 2-x = 2x - (1/2)x2 + C.
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The integral of arcsin(x) dx is x arcsin(x) + (1-x2)1/2 + C.
x3 /12 + 16x + c
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