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Trig with Partial Fractions

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Wize University Calculus 1 Textbook > Integration Techniques

Partial Fractions

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Evaluate ∫cos⁡θ3sin⁡2θ+2sin⁡θdθ\displaystyle\int\frac{\cos\theta}{3\sin^2\theta + 2\sin\theta}d\theta



More Partial Fractions Questions:
Practice Question: Partial Fraction
Compute ∫3x2−1x4+x3  ⁣dx{\displaystyle\int}\frac{3x^2-1}{x^4+x^3}\de{x}.
Practice: Partial Fractions with A and B
Q:\textbf{Q:} Find∫x2−2x−3(x2−9)(x−4)dx\displaystyle\int\frac{x^2-2x-3}{\left(x^2-9\right)\left(x-4\right)}dx
Evaluate ∫x2−92x3+x2−15x dx\displaystyle\int\frac{x^{2}-9}{2x^3+x^2-15x} \ dx and write the answer as a single logarithm.
If 9x−3x3+2x2−5x−6=Ax+1+Bx−2−Cx+3\displaystyle\frac{9x-3}{x^3+2x^2-5x-6}=\frac{A}{x+1}+\frac{B}{x-2}-\frac{C}{x+3} find the values of AA , BB and CC.
Trig with Partial Fractions
Evaluate ∫cos⁡θ3sin⁡2θ+2sin⁡θdθ\displaystyle\int\frac{\cos\theta}{3\sin^2\theta + 2\sin\theta}d\theta
Practice: Partial Fractions with A, B and C
Q:\textbf{Q:} Find ∫2x3−3x+2x3−x2−2x dx\displaystyle\int\frac{2x^3-3x+2}{x^3-x^2-2x} \ dx
Practice: Partial Fractions with A and B
Q:\textbf{Q:} Find∫x2−2x−3(x2−9)(x−4)dx\displaystyle\int\frac{x^2-2x-3}{\left(x^2-9\right)\left(x-4\right)}dx
Evaluate the integral ∫4x2−3xdx\displaystyle\int_{ }^{ }\frac{4}{x^2-3x}dx. Write your answer as a single logarithm.
(a) ln⁡∣(xx−3)43∣+C\ln\left|\left(\frac{x}{x-3}\right)^{\frac{4}{3}}\right|+C (b) ln⁡∣(x−3x)−23∣+C\ln\left|\left(\frac{x-3}{x}\right)^{-\frac{2}{3}}\right|+C (c) ln⁡∣(xx−3)23∣+C\ln\left|\left(\frac{x}{x-3}\right)^{\frac{2}{3}}\right|+C (d) ln⁡∣(x−3x)43∣+C\ln\left|\left(\frac{x-3}{x}\right)^{\frac{4}{3}}\right|+C
Practice Question: Partial Fraction
Practice Question
Compute ∫3x2−1x4+x3  ⁣dx{\displaystyle\int}\frac{3x^2-1}{x^4+x^3}\de{x}.
Evaluate ∫x(x+1)2(x2+4)dx\int_{ }^{ }\frac{x}{\left(x+1\right)^2\left(x^2+4\right)}dx
Evaluate ∫xsec⁡2xdx\int_{ }^{ }x\sec^2xdx
Practice Question: Partial Fraction
Practice Question
Compute ∫3x2−1x4+x3  ⁣dx{\displaystyle\int}\frac{3x^2-1}{x^4+x^3}\de{x}.
Rewrite the integral ∫27x2−15x−610x3−x2−3x dx\displaystyle \int_{ }^{ }\frac{27x^2-15x-6}{10x^3-x^2-3x} \ dx in partial fraction decomposition form. (Do not solve)
Evaluate the integral ∫4x2−3xdx\displaystyle\int_{ }^{ }\frac{4}{x^2-3x}dx.
Evaluate ∫x2−92x3+x2−15x dx\displaystyle\int\frac{x^{2}-9}{2x^3+x^2-15x} \ dx and write the answer as a single logarithm.
If 9x−3x3+2x2−5x−6=Ax+1+Bx−2−Cx+3\displaystyle\frac{9x-3}{x^3+2x^2-5x-6}=\frac{A}{x+1}+\frac{B}{x-2}-\frac{C}{x+3} find the values of AA , BB and CC.
Practice: Partial Fractions with A, B and C
Q:\textbf{Q:} Find ∫2x3−3x+2x3−x2−2x dx\displaystyle\int\frac{2x^3-3x+2}{x^3-x^2-2x} \ dx
Practice: Partial Fractions with A and B
Find∫x2−2x−3(x2−9)(x−4)dx\displaystyle\int\frac{x^2-2x-3}{\left(x^2-9\right)\left(x-4\right)}dx