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# AQA A-level Maths Methods of integration

Integration by parts is a special emthod of integration which is used when two functions are being multiplied. They are defined as u and v accordingly, and the given formula is used to evaluate the interval.

Integration by substitution is a method to evaluate integrals by changing the variables. This method can be used when the integral is of the given form.

When the integrand is in the form of a proper fraction, the integral should be rewritten as partial fractions and then integrated using the given result.

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Use integration by parts to evaluate ∫x(1 + cosx)dx.

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Without expanding, evaluate ∫x³(x − 10) dx.

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Integrate ∫2xcos(x²)dx.

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Use integration by substitution to find ∫5x⁴cos(x⁵)dx.

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Evaluate ∫20sin(4x) dx.

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Solve the following integral: ∫5x⁴/(x⁵ + 10)dx.

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Determine the following integral: ∫(3x + 10)/(2x + 1)²dx.

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Integrate ∫(24 + 4x)/(x − 4)(x − 3)dx using partial fractions.

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