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Popular Calculus Problems

integral of ((x^2+3x-5)/(x-3))	\int\:(\frac{x^{2}+3x-5}{x-3})dx
integral of 2+x^2	\int\:2+x^{2}dx
derivative of y/(3x)	\frac{d}{dx}(\frac{y}{3x})
(dy)/(dx)=-2y,y(0)=3	\frac{dy}{dx}=-2y,y(0)=3
derivative of (3x^2+ln(x)*(5x^3)^x)	\frac{d}{dx}((3x^{2}+\ln(x))\cdot\:(5x^{3})^{x})
integral of 7sin^5(x)cos(x)	\int\:7\sin^{5}(x)\cos(x)dx
limit as x approaches infinity of (3x-2)/(6x+1)	\lim\:_{x\to\:\infty\:}(\frac{3x-2}{6x+1})
derivative of f(x)=arccot(e^x)	derivative\:f(x)=\arccot(e^{x})
derivative of y=x^2+x^{-2}+7x-1	derivative\:y=x^{2}+x^{-2}+7x-1
integral of x^3e^{3x^4}	\int\:x^{3}e^{3x^{4}}dx
derivative of tan(3x-4y)	\frac{d}{dx}(\tan(3x-4y))
(dy)/(dx)+2xy= x/(y^2)	\frac{dy}{dx}+2xy=\frac{x}{y^{2}}
integral of cot(18x)	\int\:\cot(18x)dx
derivative of x^2+10x	\frac{d}{dx}(x^{2}+10x)
inverse oflaplace 1/((s(s^2+1)))	inverselaplace\:\frac{1}{(s(s^{2}+1))}
d/(ds)(s^3)	\frac{d}{ds}(s^{3})
sum from n=0 to infinity of (5^n)/(6^n)	\sum\:_{n=0}^{\infty\:}\frac{5^{n}}{6^{n}}
x^2y^'+3xy=1	x^{2}y^{\prime\:}+3xy=1
derivative of x^6-4e^x	derivative\:x^{6}-4e^{x}
integral of 4/(sqrt(x))+4sqrt(x)	\int\:\frac{4}{\sqrt{x}}+4\sqrt{x}dx
integral of x*x^2	\int\:x\cdot\:x^{2}dx
e^xyy^'=e^{-y}+e^{-2x-y}	e^{x}yy^{\prime\:}=e^{-y}+e^{-2x-y}
derivative of (2x)^x	derivative\:(2x)^{x}
integral of 2/(16+3x^2)	\int\:\frac{2}{16+3x^{2}}dx
derivative of regardsp I/(2p)	derivative\:regardsp\frac{I}{2p}
integral of 1/(4(1-x)^2)	\int\:\frac{1}{4(1-x)^{2}}dx
(d^2y)/(dx^2)=4x	\frac{d^{2}y}{dx^{2}}=4x
integral of (6x^2+x+6)/((x^2+1)^2)	\int\:\frac{6x^{2}+x+6}{(x^{2}+1)^{2}}dx
derivative of ln(x-4)	derivative\:\ln(x-4)
derivative of ln(sin(4x^3+6x^2+8))	\frac{d}{dx}(\ln(\sin(4x^{3}+6x^{2}+8)))
integral of (2x+5)/(x^2)	\int\:\frac{2x+5}{x^{2}}dx
integral of 1/((x^2+4x+5))	\int\:\frac{1}{(x^{2}+4x+5)}dx
derivative of 4-(600/(x^2))	\frac{d}{dx}(4-\frac{600}{x^{2}})
normal of y=2x^2,(-1,2)	normal\:y=2x^{2},(-1,2)
(\partial)/(\partial x)(-2e^x)	\frac{\partial\:}{\partial\:x}(-2e^{x})
derivative of-(2x^2/(5y^2))	\frac{d}{dx}(-\frac{2x^{2}}{5y^{2}})
y^'=((1-x))/y	y^{\prime\:}=\frac{(1-x)}{y}
derivative of (u^{-2}+u^{-3})(u^5+5u^2)	derivative\:(u^{-2}+u^{-3})(u^{5}+5u^{2})
derivative of tan^2(xθ)	\frac{d}{dx}(\tan^{2}(xθ))
integral from 1 to e^5 of 5/x	\int\:_{1}^{e^{5}}\frac{5}{x}dx
tangent of f(x)=1+sqrt(4-x),\at x=2	tangent\:f(x)=1+\sqrt{4-x},\at\:x=2
limit as x approaches infinity of (x)3	\lim\:_{x\to\:\infty\:}((x)3)
taylor cos(2x),0	taylor\:\cos(2x),0
(\partial)/(\partial t)(rcos(t)sin(s))	\frac{\partial\:}{\partial\:t}(r\cos(t)\sin(s))
derivative of x(x-4^3)	\frac{d}{dx}(x(x-4)^{3})
(x/(x^3-1))^'	(\frac{x}{x^{3}-1})^{\prime\:}
derivative of (4-4x/(3x^{2/3)})	\frac{d}{dx}(\frac{4-4x}{3x^{\frac{2}{3}}})
derivative of e^{2x}+1	derivative\:e^{2x}+1
integral from 0 to infinity of (e^x)/(1+e^x)	\int\:_{0}^{\infty\:}\frac{e^{x}}{1+e^{x}}dx
tangent of f(x)=4x^2+3x+6,(-4,58)	tangent\:f(x)=4x^{2}+3x+6,(-4,58)
critical f(x)=In(2x+1)	critical\:f(x)=In(2x+1)
integral of sec^4(x)tan^2(x)	\int\:\sec^{4}(x)\tan^{2}(x)dx
integral of 1/(sqrt(x^2-3x+2))	\int\:\frac{1}{\sqrt{x^{2}-3x+2}}dx
(x^2-1)(dy)/(dx)+2y=(x+1)^2	(x^{2}-1)\frac{dy}{dx}+2y=(x+1)^{2}
derivative of f(x)=(2x+3)^2	derivative\:f(x)=(2x+3)^{2}
integral from 0 to 2 of 2x^3sqrt(x^2+4)	\int\:_{0}^{2}2x^{3}\sqrt{x^{2}+4}dx
limit as x approaches 1 of x^3-3	\lim\:_{x\to\:1}(x^{3}-3)
tangent of f(x)=x^2+x,\at x=-1,x=2	tangent\:f(x)=x^{2}+x,\at\:x=-1,x=2
slope of (8.7)(-6.7)	slope\:(8.7)(-6.7)
sum from n=1 to infinity of 3/(n^2+4)	\sum\:_{n=1}^{\infty\:}\frac{3}{n^{2}+4}
taylor 1/(1-ax),0	taylor\:\frac{1}{1-ax},0
derivative of (x^3/3-x^2-3x+1)	\frac{d}{dx}(\frac{x^{3}}{3}-x^{2}-3x+1)
limit as x approaches 2 of-x^2+5x-2	\lim\:_{x\to\:2}(-x^{2}+5x-2)
derivative of (x-3)/(sqrt(x)-\sqrt{3)}	derivative\:\frac{x-3}{\sqrt{x}-\sqrt{3}}
integral of 4xcos(5x)	\int\:4x\cos(5x)dx
integral of x^2-7x+3	\int\:x^{2}-7x+3dx
integral of 1/(nsqrt(ln(n)))	\int\:\frac{1}{n\sqrt{\ln(n)}}
tangent of sqrt(x+5),\at x=1	tangent\:\sqrt{x+5},\at\:x=1
integral of e^{tan(9x)}sec^2(9x)	\int\:e^{\tan(9x)}\sec^{2}(9x)dx
tangent of f(x)=x^2+15x+56,\at x=2	tangent\:f(x)=x^{2}+15x+56,\at\:x=2
area 6x,x((sqrt(21^2)-x^2))	area\:6x,x((\sqrt{21^{2}}-x^{2}))
tangent of y=e^xsin(x),(0,0)	tangent\:y=e^{x}\sin(x),(0,0)
integral of x^{-1}+x^{1/3}+5/3	\int\:x^{-1}+x^{\frac{1}{3}}+\frac{5}{3}dx
derivative of 1/2 x^{-1/2}	\frac{d}{dx}(\frac{1}{2}x^{-\frac{1}{2}})
integral of 50-6.3e^{0.9x}	\int\:50-6.3e^{0.9x}dx
integral of (3x+2)^5	\int\:(3x+2)^{5}dx
derivative of f(x)= x/(sqrt(x^2+1))	derivative\:f(x)=\frac{x}{\sqrt{x^{2}+1}}
(\partial)/(\partial x)(8x(x^2+y^2)^{-1/2})	\frac{\partial\:}{\partial\:x}(8x(x^{2}+y^{2})^{-\frac{1}{2}})
tangent of f(x)=sqrt(x^2+13),\at x=6	tangent\:f(x)=\sqrt{x^{2}+13},\at\:x=6
(dy)/(dx)=2y+34x+52	\frac{dy}{dx}=2y+34x+52
limit as x approaches 0+of log_{1/e}(x)	\lim\:_{x\to\:0+}(\log_{\frac{1}{e}}(x))
(2y^2+3xy)+(2xy+x^2)(dy)/(dx)=0	(2y^{2}+3xy)+(2xy+x^{2})\frac{dy}{dx}=0
integral from 1 to 3 of x^2e^{x^3-1}	\int\:_{1}^{3}x^{2}e^{x^{3}-1}dx
integral of 2xsin(x^2)+1/(x^2)sin(1/x)	\int\:2x\sin(x^{2})+\frac{1}{x^{2}}\sin(\frac{1}{x})dx
tangent of y= 7/(sin(x)+cos(x)),(0,7)	tangent\:y=\frac{7}{\sin(x)+\cos(x)},(0,7)
derivative of 2^{3x-1}	\frac{d}{dx}(2^{3x-1})
tangent of y= x/(1+x^2),(3,0.3)	tangent\:y=\frac{x}{1+x^{2}},(3,0.3)
limit as x approaches 0+of 2/x-2/(\|x\|)	\lim\:_{x\to\:0+}(\frac{2}{x}-\frac{2}{\left\|x\right\|})
derivative of cxe^{3x}	\frac{d}{dx}(cxe^{3x})
d/(dt)(sin(t)+tcos(t))	\frac{d}{dt}(\sin(t)+t\cos(t))
derivative of ln((6x+4(3x^2+2)))	\frac{d}{dx}(\ln((6x+4)(3x^{2}+2)))
integral of ln(11x)	\int\:\ln(11x)dx
integral from-2 to-1 of x^2e^{x^3+8}	\int\:_{-2}^{-1}x^{2}e^{x^{3}+8}dx
derivative of-x^pi	\frac{d}{dx}(-x^{π})
integral of (x+3)/(sqrt(1-x^2))	\int\:\frac{x+3}{\sqrt{1-x^{2}}}dx
(\partial)/(\partial x)((3x+2y)e^{x/y})	\frac{\partial\:}{\partial\:x}((3x+2y)e^{\frac{x}{y}})
limit as x approaches 1 of sin^2(x-1)	\lim\:_{x\to\:1}(\sin^{2}(x-1))
integral of 1/(3y+2)	\int\:\frac{1}{3y+2}dy
integral of (xtan(x^2))/(cos(x^2))	\int\:\frac{x\tan(x^{2})}{\cos(x^{2})}dx
(\partial)/(\partial x)(4y^3cos(5x))	\frac{\partial\:}{\partial\:x}(4y^{3}\cos(5x))

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