Integration by Substitution

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Integration of the form

Put g(x) = t

Differentiating g(x) with respect to t, we have

g'(x) dx = dt

F(t) + C

F(g(x)) + C

Note 1:

Note 2:

Example:

Suggested answer:

Put tanx = t such that sec²xdx = dt

Integration using trigonometric identities

When the integrand consists of trigonometric function, we use suitable trigonometric identities to simplify the function so that it can be integrated. Few identities are given below for ready reference.

(1)

(2)

(3)

(4)

(5)

(7)

(8)

Example:

Integrate the function sinx. sin2x sin3x.

Suggested answer: