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OCR A-level Maths Integration of exponentials and logarithms

Integration of exponentials and logarithms

This page covers the following topics:

1. Integrating basic exponent
2. Integrating exponents
3. Integrating natural logarithm
4. Integrating logarithms

To find the integral of equations or variables in the form eΛ£, use the following rule.

Integrating basic exponent

Integrate variables in the form aΛ£ using the exponentials rule. Integrate 2 functions multiplied together by parts; for u, choose the function that is simpler when differentiated.

Integrating exponents

Integrate variables in the form lnx using integration by parts: ∫ u (dv/dx) dx = uv βˆ’ ∫ v (du/dx) dx. Let dv/dx = 1 and u = the variable in the form lnx.

Integrating natural logarithm

Integrate logarithmic functions using integration by parts: ∫ u (dv/dx) dx = uv βˆ’ ∫ v (du/dx) dx. Let dv/dx = 1 and u = the logarithmic function.

Integrating logarithms

1

Evaluate ∫ 5ˣ ⁻ ² + 4²ˣ dx.

Evaluate ∫ 5ˣ ⁻ ² + 4²ˣ dx.

2

Find ∫ xe²ˣ dx.

Find ∫ xe²ˣ dx.

3

What is ∫ 5ln(2x + 1) dx? Use the substitution a = 2x + 1.

What is ∫ 5ln(2x + 1) dx? Use the substitution a = 2x + 1.

4

Integrate (eΛ£ βˆ’ 2)Β²/eΒ²Λ£ dx.

Integrate (eΛ£ βˆ’ 2)Β²/eΒ²Λ£ dx.

5

Integrate ∫ 5ᡉˣ dx using the substitution u = ex.

Integrate ∫ 5ᡉˣ dx using the substitution u = ex.

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