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Popular Calculus Problems

cos(x)(dy)/(dx)+ysin(x)=1	\cos(x)\frac{dy}{dx}+y\sin(x)=1
limit as x approaches 0 of log_{1/2}(x)	\lim\:_{x\to\:0}(\log_{\frac{1}{2}}(x))
derivative of (x^3)/(x+1)	derivative\:\frac{x^{3}}{x+1}
integral of 18e^x	\int\:18e^{x}dx
integral from 0 to 64 of 5/(x^{2/3)}	\int\:_{0}^{64}\frac{5}{x^{\frac{2}{3}}}dx
integral from-pi/4 to 0 of 8sec^3(x)	\int\:_{-\frac{π}{4}}^{0}8\sec^{3}(x)dx
(\partial)/(\partial x)(3x^2+2xy+y^2-11)	\frac{\partial\:}{\partial\:x}(3x^{2}+2xy+y^{2}-11)
laplacetransform 15t^3	laplacetransform\:15t^{3}
f(x)=sin(xcos(x))	f(x)=\sin(x\cos(x))
t(dy)/(dt)+2y=sin(t)	t\frac{dy}{dt}+2y=\sin(t)
integral from 0 to 3 of (e^x)	\int\:_{0}^{3}(e^{x})dx
integral of (4x^3+5x)e^{x^2}	\int\:(4x^{3}+5x)e^{x^{2}}dx
integral of (x^2)/(x^{3+1)}	\int\:\frac{x^{2}}{x^{3+1}}dx
derivative of 1/x	derivative\:\frac{1}{x}
derivative of ln(cosh(5x))	\frac{d}{dx}(\ln(\cosh(5x)))
derivative of (4+x/(xe^x))	\frac{d}{dx}(\frac{4+x}{xe^{x}})
integral of 1/3 e^t	\int\:\frac{1}{3}e^{t}dt
derivative of f(x)=ln((5x+3)/(5x-3))	derivative\:f(x)=\ln(\frac{5x+3}{5x-3})
x^2+x(dy)/(dx)=y	x^{2}+x\frac{dy}{dx}=y
(\partial)/(\partial y)(-3y)	\frac{\partial\:}{\partial\:y}(-3y)
y^'+t/(t^2-16)y=(e^t)/(t-9)	y^{\prime\:}+\frac{t}{t^{2}-16}y=\frac{e^{t}}{t-9}
sum from n=0 to infinity of cos(npi)	\sum\:_{n=0}^{\infty\:}\cos(nπ)
area x=2-y^2,x=-y	area\:x=2-y^{2},x=-y
integral from 0 to infinity of 8/(x^2+4)	\int\:_{0}^{\infty\:}\frac{8}{x^{2}+4}dx
derivative of x*sqrt(x^2+1)	\frac{d}{dx}(x\cdot\:\sqrt{x^{2}+1})
tangent of y=xsqrt(x),(1,1)	tangent\:y=x\sqrt{x},(1,1)
derivative of x/(sin(x))	\frac{d}{dx}(\frac{x}{\sin(x)})
(\partial)/(\partial x)(x^{1/4})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{4}})
limit as x approaches 1 of 2x+3	\lim\:_{x\to\:1}(2x+3)
integral of cos(2x)cos(6x)	\int\:\cos(2x)\cos(6x)dx
integral from-r to r of 4(r^2-x^2)	\int\:_{-r}^{r}4(r^{2}-x^{2})dx
derivative of (4x)^{8x}	derivative\:(4x)^{8x}
derivative of (5x^3/4-2/(5x^3))	\frac{d}{dx}(\frac{5x^{3}}{4}-\frac{2}{5x^{3}})
derivative of f(x)=e^{7x}	derivative\:f(x)=e^{7x}
integral of (ln(x^2))	\int\:(\ln(x^{2}))dx
integral of (((x^m-x^n)^2)/(sqrt(x)))	\int\:(\frac{(x^{m}-x^{n})^{2}}{\sqrt{x}})dx
(\partial)/(\partial y)(4x^2+2xy+y^2-8)	\frac{\partial\:}{\partial\:y}(4x^{2}+2xy+y^{2}-8)
derivative of x^5e^{xy}+3x	\frac{d}{dx}(x^{5}e^{xy}+3x)
f(x)=tan(5x)	f(x)=\tan(5x)
area \|3x\|,x^2-4	area\:\left\|3x\right\|,x^{2}-4
derivative of ln(sqrt(((x-3))/(x-1)))	derivative\:\ln(\sqrt{\frac{(x-3)}{x-1}})
integral from 1 to 4 of 4/x	\int\:_{1}^{4}\frac{4}{x}dx
integral of t^3cos(t^2)	\int\:t^{3}\cos(t^{2})dt
limit as x approaches 5+of (5-x)/(\|5-x\|)	\lim\:_{x\to\:5+}(\frac{5-x}{\left\|5-x\right\|})
derivative of ln(4x+7)	derivative\:\ln(4x+7)
integral of ((3+e^x)^2)/(e^x)	\int\:\frac{(3+e^{x})^{2}}{e^{x}}dx
(\partial)/(\partial x)(-ysin(x))	\frac{\partial\:}{\partial\:x}(-y\sin(x))
derivative of (sin(2x)/(tan(x)))	\frac{d}{dx}(\frac{\sin(2x)}{\tan(x)})
taylor 1/((x+2))	taylor\:\frac{1}{(x+2)}
integral from 2 to 3 of t^3	\int\:_{2}^{3}t^{3}dt
integral of 1/(\sqrt[4]{x+2)}	\int\:\frac{1}{\sqrt[4]{x+2}}dx
derivative of x+(64/x)	\frac{d}{dx}(x+\frac{64}{x})
integral of 3/(x^2(x^2+25))	\int\:\frac{3}{x^{2}(x^{2}+25)}dx
integral of 1/(36+x^2)	\int\:\frac{1}{36+x^{2}}dx
derivative of (27)/(x^2+9)	derivative\:\frac{27}{x^{2}+9}
(\partial)/(\partial x)(-2e^{4y-x^2-y^2}x)	\frac{\partial\:}{\partial\:x}(-2e^{4y-x^{2}-y^{2}}x)
limit as x approaches infinity of x-6	\lim\:_{x\to\:\infty\:}(x-6)
area (8cos(pix)),(8x^2-2),[-0.5,0.5]	area\:(8\cos(πx)),(8x^{2}-2),[-0.5,0.5]
(\partial)/(\partial y)((x-4)ln(xy))	\frac{\partial\:}{\partial\:y}((x-4)\ln(xy))
limit as θ approaches 0 of sin(θ)	\lim\:_{θ\to\:0}(\sin(θ))
derivative of 1/(2sqrt(r))+1/(8r^{7/8)}	derivative\:\frac{1}{2\sqrt{r}}+\frac{1}{8r^{\frac{7}{8}}}
integral from 0 to ln(4) of (e^x)/(sqrt(e^{2x)+25)}	\int\:_{0}^{\ln(4)}\frac{e^{x}}{\sqrt{e^{2x}+25}}dx
derivative of ln(csc(x-tan(x)))	\frac{d}{dx}(\ln(\csc(x)-\tan(x)))
limit as x approaches-infinity of 1/x+3	\lim\:_{x\to\:-\infty\:}(\frac{1}{x}+3)
derivative of 4xe^{3x}	\frac{d}{dx}(4xe^{3x})
derivative of x/(sin(x+cos(x)))	\frac{d}{dx}(\frac{x}{\sin(x)+\cos(x)})
derivative of e^{5x}cos(3x)	\frac{d}{dx}(e^{5x}\cos(3x))
derivative of (x^4/(3-x^3))	\frac{d}{dx}(\frac{x^{4}}{3-x^{3}})
integral from 0 to pi/3 of 1sec^2(x)	\int\:_{0}^{\frac{π}{3}}1\sec^{2}(x)dx
integral of 5/(xln(4x))	\int\:\frac{5}{x\ln(4x)}dx
derivative of-4e^{-4x}	\frac{d}{dx}(-4e^{-4x})
derivative of sqrt(7x-8)	\frac{d}{dx}(\sqrt{7x-8})
sum from n=0 to infinity of (400)(0.1)^n	\sum\:_{n=0}^{\infty\:}(400)(0.1)^{n}
(dy)/(dx)=(x^2+2)/(3y^2)	\frac{dy}{dx}=\frac{x^{2}+2}{3y^{2}}
(x^2+x)^'	(x^{2}+x)^{\prime\:}
derivative of ((x^2)/(sin(x)))	\frac{d}{dx}(\frac{(x^{2})}{\sin(x)})
y^'-e^{6x+y}=0	y^{\prime\:}-e^{6x+y}=0
integral of x(x+1)^4	\int\:x(x+1)^{4}dx
(arcsin(2x))^'	(\arcsin(2x))^{\prime\:}
derivative of y=(arctan(3x))2	derivative\:y=(\arctan(3x))2
y^{''}-9y=e^{3x}	y^{\prime\:\prime\:}-9y=e^{3x}
derivative of f(x)=x^{2/3}(x^2-4)	derivative\:f(x)=x^{\frac{2}{3}}(x^{2}-4)
derivative of 4x^3-x^2-4x+3	\frac{d}{dx}(4x^{3}-x^{2}-4x+3)
derivative of {y}(θ,xtan(θ))	\frac{d}{dx}({y}(θ,x)\tan(θ))
y(dy)/(dx)-y^3=y^2ln(x)	y\frac{dy}{dx}-y^{3}=y^{2}\ln(x)
derivative of (x-2^2+2)	\frac{d}{dx}((x-2)^{2}+2)
y^'+5y=e^{-3t}	y^{\prime\:}+5y=e^{-3t}
inverse oflaplace (s+2)/((s-1)(s+3)^2)	inverselaplace\:\frac{s+2}{(s-1)(s+3)^{2}}
tangent of 5x-x^2	tangent\:5x-x^{2}
integral from 0 to 1 of 23((e^{1/x})/(x^3))	\int\:_{0}^{1}23(\frac{e^{\frac{1}{x}}}{x^{3}})dx
limit as x approaches-4 of 1/(x+4)	\lim\:_{x\to\:-4}(\frac{1}{x+4})
integral of (sqrt(x+1))/(x+10)	\int\:\frac{\sqrt{x+1}}{x+10}dx
area f(x)=x^2,(0,3)	area\:f(x)=x^{2},(0,3)
integral of 1/(e^xsqrt(e^{2x)-9)}	\int\:\frac{1}{e^{x}\sqrt{e^{2x}-9}}dx
area sin(x),0,2pi	area\:\sin(x),0,2π
integral of x^{15}	\int\:x^{15}dx
derivative of (7x^2-12xe^x)	\frac{d}{dx}((7x^{2}-12x)e^{x})
integral of (x^2-9)^5(2x)	\int\:(x^{2}-9)^{5}(2x)dx
(\partial)/(\partial y)(4x^3-5x^2+8x)	\frac{\partial\:}{\partial\:y}(4x^{3}-5x^{2}+8x)
(e^{-x}sin(x))^'	(e^{-x}\sin(x))^{\prime\:}

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