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Popular Calculus Problems

integral of (x^2)/(x-5)	\int\:\frac{x^{2}}{x-5}dx
(x^3+y^3)dx-xy^2dy=0	(x^{3}+y^{3})dx-xy^{2}dy=0
derivative of (x^2ln(sqrt(x))/(1+2x))	\frac{d}{dx}(\frac{x^{2}\ln(\sqrt{x})}{1+2x})
derivative of sqrt(x-7)	derivative\:\sqrt{x-7}
-10x^2y+(dy)/(dx)=-7x^2	-10x^{2}y+\frac{dy}{dx}=-7x^{2}
integral of 1000x	\int\:1000xdx
integral from 0 to 1 of (4x)/((x^2+1)^2)	\int\:_{0}^{1}\frac{4x}{(x^{2}+1)^{2}}dx
limit as x approaches 5 of (3x+5)/(5x+6)	\lim\:_{x\to\:5}(\frac{3x+5}{5x+6})
integral of 3/((x^2+1)^2)	\int\:\frac{3}{(x^{2}+1)^{2}}dx
integral of (inx)/(x^2)	\int\:\frac{inx}{x^{2}}dx
d/(dt)(3sin^3(t))	\frac{d}{dt}(3\sin^{3}(t))
7(dy)/(dx)=y^2	7\frac{dy}{dx}=y^{2}
tangent of f(x)=3x^3-x^2+4,(1,6)	tangent\:f(x)=3x^{3}-x^{2}+4,(1,6)
derivative of-6/5 e^{-20x}	\frac{d}{dx}(-\frac{6}{5}e^{-20x})
integral of e^{3x}-sin(x)+7/(1+x^2)	\int\:e^{3x}-\sin(x)+\frac{7}{1+x^{2}}dx
(\partial)/(\partial x)(ln(x^2+2y^2+2))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+2y^{2}+2))
y^'t^4=0	y^{\prime\:}t^{4}=0
integral from 0 to pi of x^2sin(x)	\int\:_{0}^{π}x^{2}\sin(x)dx
integral of (-2/(x^2)+3sqrt(x))	\int\:(-\frac{2}{x^{2}}+3\sqrt{x})dx
integral of 1/(sqrt(3-x^2-2x))	\int\:\frac{1}{\sqrt{3-x^{2}-2x}}dx
integral of tan(sqrt(x-7)) 1/(sqrt(x-7))	\int\:\tan(\sqrt{x-7})\frac{1}{\sqrt{x-7}}dx
integral of e^{ax+7}	\int\:e^{ax+7}dx
(\partial)/(\partial y)(-x)	\frac{\partial\:}{\partial\:y}(-x)
tangent of f(x)=x^4-17x^2+16,\at x=1	tangent\:f(x)=x^{4}-17x^{2}+16,\at\:x=1
area sin^2(x),sin^3(x),[0,pi]	area\:\sin^{2}(x),\sin^{3}(x),[0,π]
area y=2x^3,x=0,x=2	area\:y=2x^{3},x=0,x=2
derivative of ln\|ln(3x\|)	\frac{d}{dx}(\ln\left\|\ln(3x)\right\|)
derivative of e^{2x-4}	\frac{d}{dx}(e^{2x-4})
derivative of f(x)=(2x)/(x^2+4)	derivative\:f(x)=\frac{2x}{x^{2}+4}
integral of-9x^2sec(3x^3+1)tan(3x^3+1)	\int\:-9x^{2}\sec(3x^{3}+1)\tan(3x^{3}+1)dx
integral of inx	\int\:inxdx
(\partial)/(\partial x)(y{f}(x)+2x^3)	\frac{\partial\:}{\partial\:x}(y{f}(x)+2x^{3})
derivative of e^{1-x}*(5-x^2)	derivative\:e^{1-x}\cdot\:(5-x^{2})
derivative of f(x)=(7x^4-6x^3-5x)^8	derivative\:f(x)=(7x^{4}-6x^{3}-5x)^{8}
integral of 120x*(2x+1)^4	\int\:120x\cdot\:(2x+1)^{4}dx
integral of 1/3 e^{-x/2}(x+1)	\int\:\frac{1}{3}e^{-\frac{x}{2}}(x+1)dx
integral of sec^8(t)anx	\int\:\sec^{8}(t)anxdx
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
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})
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 (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}
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)}
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
(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
integral of (sqrt(x^2-9))/(x^3)	\int\:\frac{\sqrt{x^{2}-9}}{x^{3}}dx
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 of 5/(sqrt(x+6))	\int\:\frac{5}{\sqrt{x+6}}dx
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

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