Integrals of the type ∫f(x)(f(x))^n dx (HSC SSCE Mathematics Extension 1): Flashcards
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What substitution for integrals of form f'(x)(f(x))^n?
What substitution for integrals of form f'(x)(f(x))^n?
Let u = f(x), du = f'(x) dx
General result after substituting u for ∫ u^n du?
General result after substituting u for ∫ u^n du?
∫ u^n du = u^(n+1)/(n+1) + C
Evaluate ∫ x/(x^2+1) dx using substitution
Evaluate ∫ x/(x^2+1) dx using substitution
1/2 ln|x^2+1| + C
Substitute u for which part?
Substitute u for which part?
Set u = f(x), du = f'(x) dx
Solve ∫2x(x^2+1)^3 dx
Solve ∫2x(x^2+1)^3 dx
(x^2+1)^4/4 + C
How integrate when n = -1?
How integrate when n = -1?
Result is constant*ln|f(x)| + C
Result of ∫ e^{2x}(e^{2x}+1)^{-2} dx?
Result of ∫ e^{2x}(e^{2x}+1)^{-2} dx?
-1/(2(e^{2x}+1)) + C
What substitution solves ∫ f'(x)(f(x))^n dx?
What substitution solves ∫ f'(x)(f(x))^n dx?
u = f(x), du = f'(x) dx
Compute ∫2x(x^2+1)^3 dx
Compute ∫2x(x^2+1)^3 dx
(x^2 + 1)^4/4 + C
Result of ∫ f'(x)/f(x) dx?
Result of ∫ f'(x)/f(x) dx?
ln|f(x)| + C