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4.04 Further anti-differentiation

Interactive practice questions

Find $\int\left(x-5\right)^4dx$(x5)4dx, with $C$C as the constant of integration.

Easy
1min

Find $\int\frac{1}{\left(x+6\right)^3}dx$1(x+6)3dx, with $C$C as the constant of integration.

Easy
1min

Find $\int6\left(x+2\right)^2dx$6(x+2)2dx, with $C$C as the constant of integration.

Easy
1min

Find $\int\frac{4}{\left(x-5\right)^3}dx$4(x5)3dx, with $C$C as the constant of integration.

Easy
1min
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Outcomes

3.3.1.3

establish and use the formula ∫ 𝑥^𝑛 𝑑x = 1/(n+1) 𝑥^(𝑛+1)+𝑐 for 𝑛≠−1

3.3.1.4

establish and use the formula ∫ 𝑒^𝑥 𝑑x=𝑒^𝑥+c

3.3.1.6

establish and use the formulas ∫ sin(𝑥) 𝑑x = −cos(𝑥) + 𝑐𝑐 and ∫ cos(𝑥)𝑑x = sin(𝑥) + c

3.3.1.8

determine indefinite integrals of the form ∫ 𝑓(𝑎x+𝑏) 𝑑x

3.3.1.10

determine the integral of a function using information about the derivative of the given function (integration by recognition)

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