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Fill in the blank:
If F = ∫f\int_{ }^{ }f∫f and G = ∫g\int_{ }^{ }g∫g then aF + bG = ___________.
∫(af+g)\int_{ }^{ }\left(af+g\right)∫(af+g)
∫(af+bg)\int_{ }^{ }\left(af+bg\right)∫(af+bg)
Which method is used for computing antiderivatives?
Lebniz Rule
product rule
Integration by parts
Which method is suitable for computing the antiderivative of 1xlnx\frac{1}{x\ln x}xlnx1 ?
Integration by substitution
If f and g are both continuous, and F and G are the antiderivatives of f and G respectively, then
∫fG+∫Fg =FG+c\int_{ }^{ }fG+\int_{ }^{ }Fg\ =FG+c∫fG+∫Fg =FG+c
What is the name of this method for computing antiderivatives?
Which method is used for computing the antiderivatives?
If f and g are both continuous functions, and F and G are antiderivatives of f and g respectively, then
aF+bG=∫(af+bg)aF+bG=\int_{ }^{ }\left(af+bg\right)aF+bG=∫(af+bg)
What is the name of this method for computing the antiderivatives?
linearity method
Which of the following is not a method used for computing antiderivatives?
Compute the antiderivative of logx\log xlogx using integration by parts.
xlogx−x+cx\log x-x+cxlogx−x+c
xlogx+cx\log x+cxlogx+c
2x−32x^{-3}2x−3
Which method is suitable for computing the antiderivative of exex+3\frac{e^x}{e^{^x}+3}ex+3ex ?
Compute the antiderivative of 4logx4\log x4logx using integration by parts.
4(xlogx−x)+c4\left(x\log x-x\right)+c4(xlogx−x)+c
It is done.