Question

1. Evaluate each of the following integrals. If partial fraction decomposition of the rational function is needed, rewrite in terms of partial fractions, before integrating. (i) $ \int \frac{x-2}{(x+2)^2(x-1)(x-3)}dx $ (ii) $ \int \frac{x}{(x+1)(x^4-16)}dx $ (iii) $ \int \frac{x^2+2}{(x^2+9)}dx $ (iv) $ \int \sin(2x)\cos(4x)dx $ (v) $ \int \sin(x^3)2x^2dx $ (vi) $ \int \sin^4(x)\tan^3(x)dx $ (Hint: simplify to write the integrand as powers of cosine and one $ \sin x $ factor) (vii) $ \int \sqrt{3-x^2+2x}dx $ (viii) $ \int e^x\sqrt{(e^x+2)}dx $ (ix) $ \int \sqrt{(e^x+2)}dx $ (x) $ \int \cos x(\frac{1}{\sin x+2})dx $

          1. Evaluate each of the following integrals. If partial fraction decomposition of the
rational function is needed, rewrite in terms of partial fractions, before integrating.
(i) \( \int \frac{x-2}{(x+2)^2(x-1)(x-3)}dx \)
(ii) \( \int \frac{x}{(x+1)(x^4-16)}dx \)
(iii) \( \int \frac{x^2+2}{(x^2+9)}dx \)
(iv) \( \int \sin(2x)\cos(4x)dx \)
(v) \( \int \sin(x^3)2x^2dx \)
(vi) \( \int \sin^4(x)\tan^3(x)dx \) (Hint: simplify to write the integrand as powers of
cosine and one \( \sin x \) factor)
(vii) \( \int \sqrt{3-x^2+2x}dx \)
(viii) \( \int e^x\sqrt{(e^x+2)}dx \)
(ix) \( \int \sqrt{(e^x+2)}dx \)
(x) \( \int \cos x(\frac{1}{\sin x+2})dx \)

$1. Evaluate each of the following integrals. If partial fraction decomposition of the rational function is needed, rewrite in terms of partial fractions, before integrating. (i) ∫(x-2)/((x+2)^2(x-1)(x-3))dx (ii) ∫(x)/((x+1)(x^4-16))dx (iii) ∫(x^2+2)/((x^2+9))dx (iv) ∫sin(2x)cos(4x)dx (v) ∫sin(x^3)2x^2dx (vi) ∫sin^4(x)tan^3(x)dx (Hint: simplify to write the integrand as powers of cosine and one sin x factor) (vii) ∫√(3-x^2+2x)dx (viii) ∫ e^x√((e^x+2))dx (ix) ∫√((e^x+2))dx (x) ∫cos x((1)/(sin x+2))dx$

Added by Joan D.

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