Find the general indefinite integrals integral of x^(2) square root of (x^(3)+1)dx integral of pi sin x cos^(3)x dx

Adrien Jordan
2022-09-17

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asked 2021-05-11

Evaluate the line integral, where C is the given curve

C xy ds

C:$x={t}^{2},y=2t,0\le t\le 5$

C xy ds

C:

asked 2021-02-24

asked 2022-04-12

I need help computing this integral:

$\begin{array}{}\text{(1)}& {\int}_{0}^{\mathrm{\infty}}\frac{x\mathrm{cos}(ax)}{{x}^{2}+1}\mathrm{coth}(sx)\mathrm{d}x\end{array}$

$\begin{array}{}\text{(1)}& {\int}_{0}^{\mathrm{\infty}}\frac{x\mathrm{cos}(ax)}{{x}^{2}+1}\mathrm{coth}(sx)\mathrm{d}x\end{array}$

asked 2022-05-23

I'm dealing with these two integrals:

${I}_{1}={\int}_{-\pi}^{\pi}\frac{\mathrm{cos}(x)\mathrm{cos}(nx)}{(1+e\mathrm{cos}(x){)}^{3}}\mathrm{d}x,\phantom{\rule{1em}{0ex}}{I}_{2}={\int}_{-\pi}^{\pi}\frac{\mathrm{sin}(x)\mathrm{sin}(nx)}{(1+e\mathrm{cos}(x){)}^{3}}\mathrm{d}x$

is there a way to reduce them to a Hypergeometric form or to solve them analytically?

${I}_{1}={\int}_{-\pi}^{\pi}\frac{\mathrm{cos}(x)\mathrm{cos}(nx)}{(1+e\mathrm{cos}(x){)}^{3}}\mathrm{d}x,\phantom{\rule{1em}{0ex}}{I}_{2}={\int}_{-\pi}^{\pi}\frac{\mathrm{sin}(x)\mathrm{sin}(nx)}{(1+e\mathrm{cos}(x){)}^{3}}\mathrm{d}x$

is there a way to reduce them to a Hypergeometric form or to solve them analytically?

asked 2021-05-29

Find a Cartesian equation for the curve and identify it.

$r=7\mathrm{cos}(\theta )$

asked 2021-12-20

A particle travels along a straight line with a velocity of $v=(4t-3{t}^{2})\frac{m}{s}$, where t is in seconds. Determine the position of the particle when $t=4s.\text{}s=0$ when $t=0$.

asked 2022-05-11

Integrate $3{x}^{2}\ufeff-\frac{3}{2{x}^{2}}-3\mathrm{sin}(3x)+\frac{1}{2}$ with respect to x.