4.04 Further anti-differentiation

Interactive practice questions

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

Easy

1min

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

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

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

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

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