Grey Divider
Calculus, indefinite integrals?
Evaluate each of the following indefinite integrals:
(a) dx
______
cos^2 (3x)
(b) 6x^5 -2x^4 + 3x^3 + x^2 – x-2
___________________________ dx
x^3
(c) 2x^3 + 3x
_____________ dx
x^4 + 3x^2 +5
(d) 10(ln x)^4
__________ dx
x
The gray lines ( ___ ) are pretty much the divider like 1 over 2
I need to see all steps please thanks
Take ‘$’ as integral.
(a)
$1/ cos^2 (3x) dx
=$sec^2(3x)dx
=(tan(3x))/3 +c
(b) $(6x^5 -2x^4 + 3x^3 + x^2 – x -2)/x^3 dx
=$(6x^2 -2x + 3 + 1/x – 1/x^2 -(2)/x^3) dx
= 2x^3 – x^2 +3x + ln(x) + 1/x + 1/x^2 +c
(c)$(2x^3 + 3x)/(x^4 + 3x^2 +5) dx
Divide and multiply by 2 {I got to this step by differentiating the denominator}
=$(1/2)(4x^3 +6x)/(x^4 + 3x^2 +5) dx
Let (x^4 + 3x^2 +5) =t
(4x^3 +6x)dx = dt
=$ (1/2t)dt
=(1/2)ln(t) +c
=(1/2)ln(x^4 + 3x^2 +5) +c
(d)$(10(ln x)^4)/x dx
let lnx = t
(dx)/x = dt
=$10t^4 dt
=2t^5 +c
2(ln(x))^5 +c
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