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IntegrationQuestion and Answers: Page 191

Question Number 84170    Answers: 2   Comments: 0

$$\int \frac{\mathrm{dx}}{{\mathrm{x}}^3\sqrt[3]{4-{\mathrm{x}}^3}}?$$

Question Number 84030    Answers: 0   Comments: 0

$$find\int \sqrt{\frac{x+2}{x^2-x-3}}dx$$

Question Number 83984    Answers: 1   Comments: 0

$$\int {cos}^7\left(x\right)dx$$

Question Number 83961    Answers: 0   Comments: 1

$$findI=\int e^{-x}{cos}^{4}xdxandJ=\int e^{-x}{sin}^{4}xdx$$

Question Number 83960    Answers: 2   Comments: 1

$$\int \frac{\mathrm{x}-1}{\sqrt{{\mathrm{x}}^2-\mathrm{x}}}\mathrm{dx}?$$

Question Number 83927    Answers: 1   Comments: 0

$$\int \frac{sinh\left(x\right)+e^{3x}}{sinh\left(x\right)-e^x}dx$$

Question Number 83923    Answers: 1   Comments: 0

$$\int \frac{{\mathrm{x}}^2+20}{{(\mathrm{xsin}\mathrm{x}+5\cos \mathrm{x})}^2}\mathrm{dx}=?$$

Question Number 83921    Answers: 1   Comments: 0

$$\int \frac{{2\mathrm{x}}^{12}+{5\mathrm{x}}^9}{{({\mathrm{x}}^5+{\mathrm{x}}^3+1)}^3}\mathrm{dx}=?$$

Question Number 83917    Answers: 5   Comments: 0

$$find\int \frac{dx}{{(1+\sqrt{1+x^2})}^2}$$

Question Number 83899    Answers: 0   Comments: 1

$$\mathrm{Defined}\mathrm{a}\mathrm{function}\mathrm{f}\left(\mathrm{x}\right)\mathrm{such}$$$$\mathrm{that}\mathrm{f}(1-\mathrm{x})+2\mathrm{f}\left(\mathrm{x}\right)=\mathrm{nx}$$$$\mathrm{for}\mathrm{m},\mathrm{n}>1,\mathrm{the}\mathrm{value}\mathrm{of}$$$$\int \underset{1}{\stackrel{\mathrm{m}}{}}(2\mathrm{n}+6\mathrm{f}\left(\frac{\mathrm{m}}{\mathrm{x}}\right))\mathrm{dx}\mathrm{is}...$$

Question Number 83898    Answers: 0   Comments: 4

$$\int \frac{\mathrm{du}}{\sqrt{{\mathrm{u}}^2-1}-\mathrm{u}}$$

Question Number 83893    Answers: 0   Comments: 1

$$\int \frac{\mathrm{du}}{\mathrm{u}-{\mathrm{u}}^2}$$

Question Number 83852    Answers: 0   Comments: 3

$$f\left(\alpha \right)={\int }_0^{\mathrm{\infty }}\frac{e^{-\alpha x}sin\left(x\right)}{x}dx$$

Question Number 83842    Answers: 0   Comments: 4

$$\int \frac{ln\left(x\right)}{ln(6x-x^2)}dx$$

Question Number 83819    Answers: 1   Comments: 0

$$\mathrm{If}\mathrm{the}\mathrm{function}\mathrm{of}\mathrm{f}\mathrm{is}\mathrm{continous}$$$$\mathrm{in}\mathbb{R}\mathrm{and}\int \underset{0}{\stackrel{\mathrm{x}}{}}\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt}=\int \underset{\mathrm{x}}{\stackrel{1}{}}{\mathrm{t}}^2\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt}+$$$${2\mathrm{x}}^2+4\mathrm{x}+\mathrm{c},\mathrm{\forall }\mathrm{x}\in \mathbb{R}.$$$$\mathrm{The}\mathrm{value}\mathrm{of}\mathrm{constant}\mathrm{c}\mathrm{is}$$

Question Number 83807    Answers: 2   Comments: 1

$$\mathbf{Evaluate}:$$$$\int \frac{1}{{\mathbf{ax}}^2+\mathbf{bx}+\mathbf{c}}\mathbf{dx}$$

Question Number 83805    Answers: 3   Comments: 1

$${\int }_0^{\frac{\pi }{2}}\frac{{sin}^2\left(x\right)}{sin\left(x\right)+cos\left(x\right)}dx$$

Question Number 83892    Answers: 0   Comments: 0

$$\int \frac{\mathrm{du}}{\mathrm{u}-{\mathrm{u}}^2}$$

Question Number 83781    Answers: 1   Comments: 2

$$\int {}_0^{\frac{\pi }{2}}\frac{1}{4\sin {}^{2}x+5\cos {}^{2}x}dx$$

Question Number 83750    Answers: 0   Comments: 0

$$I=\int e^{x}tan\left(x\right)dx$$

Question Number 83737    Answers: 0   Comments: 0

$$\int \frac{x^3}{x^4+\cos x}dx?$$

Question Number 83713    Answers: 1   Comments: 8

$$\int \frac{dx}{\sqrt{x+\sqrt{x+\sqrt{x}}}}pleassirhelpme$$

Question Number 83691    Answers: 1   Comments: 2

$$\mathrm{evaluate}:$$$$\int \frac{\mathbf{dx}}{\mathbf{a}\mathbf{sin}\mathbf{x}+\mathbf{b}\mathbf{cos}\mathbf{x}}$$

Question Number 83675    Answers: 1   Comments: 2

$$$$$$$$$$\mathrm{evaluate}:$$$$2{\int }_0^2\frac{\sqrt{\mathrm{x}+1}}{{\mathrm{x}}^2+4}\mathrm{dx}$$$$$$$$$$

Question Number 83642    Answers: 0   Comments: 0

$$$$$$$$$$\mathfrak{Find}\mathfrak{the}\mathfrak{surface}\mathfrak{area}\mathfrak{of}\mathfrak{the}\mathfrak{solid}\mathfrak{generated}$$$$\mathfrak{by}\mathfrak{the}\mathfrak{revolution}\mathfrak{of}\mathfrak{the}\mathfrak{cardioids}\mathfrak{r}=\mathfrak{a}(1+\mathfrak{cos}\theta )\mathfrak{about}\mathfrak{the}\mathfrak{initial}\mathfrak{line}.$$

Question Number 83603    Answers: 0   Comments: 4

$$\int \frac{\mathrm{dx}}{1-2\cos \mathrm{x}}$$

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