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Fungrim entry: 463077

z1(ax+b)cdx=1a(c1)(az+b)c1\int_{z}^{\infty} \frac{1}{{\left(a x + b\right)}^{c}} \, dx = \frac{1}{a \left(c - 1\right) {\left(a z + b\right)}^{c - 1}}
Assumptions:aR  and  bR  and  cR  and  zR  and  a>0  and  az+b>0  and  c>1a \in \mathbb{R} \;\mathbin{\operatorname{and}}\; b \in \mathbb{R} \;\mathbin{\operatorname{and}}\; c \in \mathbb{R} \;\mathbin{\operatorname{and}}\; z \in \mathbb{R} \;\mathbin{\operatorname{and}}\; a > 0 \;\mathbin{\operatorname{and}}\; a z + b > 0 \;\mathbin{\operatorname{and}}\; c > 1
\int_{z}^{\infty} \frac{1}{{\left(a x + b\right)}^{c}} \, dx = \frac{1}{a \left(c - 1\right) {\left(a z + b\right)}^{c - 1}}

a \in \mathbb{R} \;\mathbin{\operatorname{and}}\; b \in \mathbb{R} \;\mathbin{\operatorname{and}}\; c \in \mathbb{R} \;\mathbin{\operatorname{and}}\; z \in \mathbb{R} \;\mathbin{\operatorname{and}}\; a > 0 \;\mathbin{\operatorname{and}}\; a z + b > 0 \;\mathbin{\operatorname{and}}\; c > 1
Fungrim symbol Notation Short description
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Powab{a}^{b} Power
Infinity\infty Positive infinity
RRR\mathbb{R} Real numbers
Source code for this entry:
    Formula(Equal(Integral(Div(1, Pow(Add(Mul(a, x), b), c)), For(x, z, Infinity)), Div(1, Mul(Mul(a, Sub(c, 1)), Pow(Add(Mul(a, z), b), Sub(c, 1)))))),
    Variables(a, b, c, z),
    Assumptions(And(Element(a, RR), Element(b, RR), Element(c, RR), Element(z, RR), Greater(a, 0), Greater(Add(Mul(a, z), b), 0), Greater(c, 1))))

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2021-03-15 19:12:00.328586 UTC