12. Integration

iGCSE (2021 Edition)

Find $y$`y` if $\frac{dy}{dx}=\left(3x+5\right)^4$`d``y``d``x`=(3`x`+5)4.

Use $C$`C` as the constant of integration.

Easy

Approx 2 minutes

If $\frac{dy}{dx}=\left(6x-5\right)^2$`d``y``d``x`=(6`x`−5)2, find the primitive, $y$`y`.

Use $C$`C` to represent any constant.

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

Find $\int\left(2x+3\right)^3dx$∫(2`x`+3)3`d``x`, with $C$`C` as the constant of integration.

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Integrate functions of the form (ax + b)^n for any rational n.