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Popular Calculus Problems

integral of-1/9 x^{-10/9}	\int\:-\frac{1}{9}x^{-\frac{10}{9}}dx
derivative of 2/(x^{13})	\frac{d}{dx}(\frac{2}{x^{13}})
integral of (tan(x)-sin(x)sin(y))	\int\:(\tan(x)-\sin(x)\sin(y))dx
tangent of f(x)=sin(x),\at x=1	tangent\:f(x)=\sin(x),\at\:x=1
integral of (x^3+1)/(x^2)	\int\:\frac{x^{3}+1}{x^{2}}dx
derivative of 3/x+5	\frac{d}{dx}(\frac{3}{x}+5)
integral of (1/(xln(x)))	\int\:(\frac{1}{x\ln(x)})dx
(\partial)/(\partial x)(xy^2-5y+6)	\frac{\partial\:}{\partial\:x}(xy^{2}-5y+6)
tangent of f(x)=6xsin(x),\at x= pi/2	tangent\:f(x)=6x\sin(x),\at\:x=\frac{π}{2}
derivative of ce^{4x}	\frac{d}{dx}(ce^{4x})
limit as x approaches infinity of 8x-32	\lim\:_{x\to\:\infty\:}(8x-32)
derivative of (e^x/(tan(x)))	\frac{d}{dx}(\frac{e^{x}}{\tan(x)})
derivative of ln(xsqrt(2-x))	derivative\:\ln(x\sqrt{2-x})
y^{''}+2y^'+2y=sin(3t)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(3t)
derivative of-cos(pix)	\frac{d}{dx}(-\cos(πx))
t^2y^'+4ty-y^3=0	t^{2}y^{\prime\:}+4ty-y^{3}=0
area x^2,sqrt(9+x)	area\:x^{2},\sqrt{9+x}
integral of csc^2(t)-2e^t	\int\:\csc^{2}(t)-2e^{t}dt
derivative of a(x-b^2)	\frac{d}{dx}(a(x-b)^{2})
derivative of (1-x^{-1/2})	\frac{d}{dx}((1-x)^{-\frac{1}{2}})
inverse oflaplace (900)/(s^2+90s+900)	inverselaplace\:\frac{900}{s^{2}+90s+900}
integral of 8sqrt(x)+6cos(x)	\int\:8\sqrt{x}+6\cos(x)dx
integral from 0 to x of e^{-u}	\int\:_{0}^{x}e^{-u}du
(1/(sin(x)))^'	(\frac{1}{\sin(x)})^{\prime\:}
integral of v^2	\int\:v^{2}dv
inverse oflaplace (2s+1)/(s^2+9)	inverselaplace\:\frac{2s+1}{s^{2}+9}
derivative of-2arcsec(x+1)	\frac{d}{dx}(-2\arcsec(x+1))
integral of sin(ax)cos(ax)	\int\:\sin(a\cdot\:x)\cos(a\cdot\:x)dx
integral of 8e^{-x}	\int\:8e^{-x}dx
(dy)/(dx)= k/x	\frac{dy}{dx}=\frac{k}{x}
(\partial)/(\partial x)(10e^{x^7y})	\frac{\partial\:}{\partial\:x}(10e^{x^{7}y})
tangent of 1.8e^{2x}-45	tangent\:1.8e^{2x}-45
derivative of y=(sqrt(x))/(6+x)	derivative\:y=\frac{\sqrt{x}}{6+x}
inverse oflaplace 5/(s^2+49)	inverselaplace\:\frac{5}{s^{2}+49}
sum from n=0 to infinity of (-5/4)^{-2n}	\sum\:_{n=0}^{\infty\:}(-\frac{5}{4})^{-2n}
limit as h approaches 0 of (a^h-1)/h	\lim\:_{h\to\:0}(\frac{a^{h}-1}{h})
y^'=(2y)/(tan(x))	y^{\prime\:}=\frac{2y}{\tan(x)}
integral from x to 10 of t^3	\int\:_{x}^{10}t^{3}dt
derivative of 8-3x	\frac{d}{dx}(8-3x)
limit as x approaches infinity of x^9	\lim\:_{x\to\:\infty\:}(x^{9})
derivative of (2x)/((1+x^2)^2)	derivative\:\frac{2x}{(1+x^{2})^{2}}
derivative of f(x)= x/(1-ln(x-7))	derivative\:f(x)=\frac{x}{1-\ln(x-7)}
area cos(x),(3x)/(2pi),[0,1]	area\:\cos(x),\frac{3x}{2π},[0,1]
y^'=((ln^2(x)))/(\sqrt[3]{x)}	y^{\prime\:}=\frac{(\ln^{2}(x))}{\sqrt[3]{x}}
derivative of y=x^2-3x	derivative\:y=x^{2}-3x
limit as x approaches-3-of h(x)	\lim\:_{x\to\:-3-}(h(x))
slope ofintercept (1.7)(6.1)	slopeintercept\:(1.7)(6.1)
derivative of arctan(x+1)	\frac{d}{dx}(\arctan(x+1))
derivative of 26(2e^{x^2}x^2+e^{x^2})	\frac{d}{dx}(26(2e^{x^{2}}x^{2}+e^{x^{2}}))
integral of (1+1/x)	\int\:(1+\frac{1}{x})dx
integral of (2x+1)/(x^2+x)	\int\:\frac{2x+1}{x^{2}+x}dx
integral of 5sin^2(x)cos^2(x)	\int\:5\sin^{2}(x)\cos^{2}(x)dx
(dy)/(dx)=yx^6sin(x^7)	\frac{dy}{dx}=yx^{6}\sin(x^{7})
derivative of f(x)=x*e^x	derivative\:f(x)=x\cdot\:e^{x}
integral from 0 to 1 of xln(x)	\int\:_{0}^{1}x\ln(x)dx
integral of 1/(x^2)sqrt(2+1/x)	\int\:\frac{1}{x^{2}}\sqrt{2+\frac{1}{x}}dx
integral of ((x^{-2}-4))/(x^3)	\int\:\frac{(x^{-2}-4)}{x^{3}}dx
integral of (2x-3)^2sqrt((2x-3)^2+4)	\int\:(2x-3)^{2}\sqrt{(2x-3)^{2}+4}dx
laplacetransform cos^2(17t)	laplacetransform\:\cos^{2}(17t)
limit as x approaches infinity of (x^{ln(n)})/(x^{ln(n)+1)}	\lim\:_{x\to\:\infty\:}(\frac{x^{\ln(n)}}{x^{\ln(n)+1}})
derivative of ln(x/y)	derivative\:\ln(\frac{x}{y})
integral of sin(2x)sin(6x)	\int\:\sin(2x)\sin(6x)dx
derivative of 3sqrt(2-x)	\frac{d}{dx}(3\sqrt{2-x})
integral from 3 to infinity of 2/(x^2-1)	\int\:_{3}^{\infty\:}\frac{2}{x^{2}-1}dx
maclaurin ln(1+z)	maclaurin\:\ln(1+z)
(\partial)/(\partial x)(42y^6x^5-30y^5x^4)	\frac{\partial\:}{\partial\:x}(42y^{6}x^{5}-30y^{5}x^{4})
integral from 1 to e^3 of (ln(x))/(x^2)	\int\:_{1}^{e^{3}}\frac{\ln(x)}{x^{2}}dx
y^'+y=e^t	y^{\prime\:}+y=e^{t}
integral of (sqrt(x^2-9))/(x^3)	\int\:\frac{\sqrt{x^{2}-9}}{x^{3}}dx
derivative of g(x)=sqrt(x)	derivative\:g(x)=\sqrt{x}
derivative of cxe^x	\frac{d}{dx}(cxe^{x})
(\partial)/(\partial x)(2x^4y^3+y)	\frac{\partial\:}{\partial\:x}(2x^{4}y^{3}+y)
integral from 0 to 2 of x(2+x^5)	\int\:_{0}^{2}x(2+x^{5})dx
derivative of 2/(cos(xcot(x)))	\frac{d}{dx}(\frac{2}{\cos(x)\cot(x)})
integral of 5/(sqrt(x+6))	\int\:\frac{5}{\sqrt{x+6}}dx
area y=x-4,y^2=2x	area\:y=x-4,y^{2}=2x
limit as x approaches+0 of xln(1/x)	\lim\:_{x\to\:+0}(x\ln(\frac{1}{x}))
simplify (sin(x))(sec(x))	simplify\:(\sin(x))(\sec(x))
integral from-1 to 1 of 1/2 (1-x^4)	\int\:_{-1}^{1}\frac{1}{2}(1-x^{4})dx
integral of (x^3+5x+1)/(x^2+5)	\int\:\frac{x^{3}+5x+1}{x^{2}+5}dx
(\partial)/(\partial x)(xe^{y/x})	\frac{\partial\:}{\partial\:x}(xe^{\frac{y}{x}})
integral of (xe^{2x})	\int\:(x\cdot\:e^{2\cdot\:x})dx
(\partial)/(\partial y)(y-ln(x^2+y^2))	\frac{\partial\:}{\partial\:y}(y-\ln(x^{2}+y^{2}))
derivative of y= 3/(x^2-1)	derivative\:y=\frac{3}{x^{2}-1}
limit as x approaches 0+of 6(cot(x)-1/x)	\lim\:_{x\to\:0+}(6(\cot(x)-\frac{1}{x}))
derivative of-e^{-2x}	\frac{d}{dx}(-e^{-2x})
tangent of f(x)=sqrt(5x+4),\at x=9	tangent\:f(x)=\sqrt{5x+4},\at\:x=9
y^{''}+10y^'+25y=2r^{-5x}	y^{\prime\:\prime\:}+10y^{\prime\:}+25y=2r^{-5x}
integral of ln(x^{1/3})	\int\:\ln(x^{\frac{1}{3}})dx
integral of (3-cos^3(x))sin(x)	\int\:(3-\cos^{3}(x))\sin(x)dx
laplacetransform 3sin(4t)	laplacetransform\:3\sin(4t)
derivative of cos(x^{ln(x^2+1}))	\frac{d}{dx}(\cos(x^{\ln(x^{2}+1)}))
limit as x approaches 0 of (x-x)/x	\lim\:_{x\to\:0}(\frac{x-x}{x})
8x^{''}+8x^'+1/4 x=0,x^'(0)=1,x(0)=2	8x^{\prime\:\prime\:}+8x^{\prime\:}+\frac{1}{4}x=0,x^{\prime\:}(0)=1,x(0)=2
derivative of (2sqrt(x)/(1-x))	\frac{d}{dx}(\frac{2\sqrt{x}}{1-x})
limit as x approaches 0 of 0/x	\lim\:_{x\to\:0}(\frac{0}{x})
integral of u^{3/2}	\int\:u^{\frac{3}{2}}du
derivative of sqrt(x)+5	\frac{d}{dx}(\sqrt{x}+5)
limit as x approaches 0+of ln(1/(8x))	\lim\:_{x\to\:0+}(\ln(\frac{1}{8x}))
derivative of 4sin^3(sqrt(x))	\frac{d}{dx}(4\sin^{3}(\sqrt{x}))

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