Indefinite Integration

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Indefinite Integration. Let f,g,hf, g, h be 3 functions such that f′(x)>0f'(x) > 0 & g(x)≥0 ∀x∈Rg(x) \geq 0\ \forall x \in R where ∫f(x)⋅g(x) dx=x44+C\int f(x) \cdot g(x)\,dx = \frac{x^4}{4} + C & ∫f(x)g(x) dx=∫g(x)h(x) dx=ln⁡∣x∣+C, x≠0\int \frac{f(x)}{g(x)}\,dx = \int \frac{g(x)}{h(x)}\,dx = \ln |x| + C,\ x \neq 0. ∫f(x)⋅g(x)⋅h(x) dx\int f(x) \cdot g(x) \cdot h(x)\,dx is equal to (a) x55+C\frac{x^5}{5} + C (b) x66+C\frac{x^6}{6} + C (c) x77+C\frac{x^7}{7} + C (d) x88+C\frac{x^8}{8} + C

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