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Popular Calculus Problems

limit as x approaches 0 of (cos(pix))/x	\lim\:_{x\to\:0}(\frac{\cos(πx)}{x})
laplacetransform te^{-3t}	laplacetransform\:te^{-3t}
derivative of (x^3-1^{100})	\frac{d}{dx}((x^{3}-1)^{100})
area y=x^4,x=y^7,1	area\:y=x^{4},x=y^{7},1
integral of sqrt(8+2x-x^2)	\int\:\sqrt{8+2x-x^{2}}dx
limit as x approaches 1+of ln\|x^2-1\|	\lim\:_{x\to\:1+}(\ln\left\|x^{2}-1\right\|)
integral from 0 to 1 of xsqrt(5x+4)	\int\:_{0}^{1}x\sqrt{5x+4}dx
integral of x^2+sin(x)	\int\:x^{2}+\sin(x)dx
integral of ((x^3))/(sqrt(4+x^2))	\int\:\frac{(x^{3})}{\sqrt{4+x^{2}}}dx
derivative of xn(x)	\frac{d}{dx}(xn(x))
integral of 1/(v^2+3v-4)	\int\:\frac{1}{v^{2}+3v-4}dv
derivative of (-4)/((7x^5+6)^6)	derivative\:\frac{-4}{(7x^{5}+6)^{6}}
laplacetransform 10t	laplacetransform\:10t
y^'=-6.2-1.8y	y^{\prime\:}=-6.2-1.8y
derivative of y=(18)/(x^4)	derivative\:y=\frac{18}{x^{4}}
derivative of sqrt(cos(e^{x^4cos(x))})	\frac{d}{dx}(\sqrt{\cos(e^{x^{4}\cos(x)})})
limit as x approaches 0 of (2\|x\|)/(3x)	\lim\:_{x\to\:0}(\frac{2\left\|x\right\|}{3x})
derivative of y=e^{9-x}	derivative\:y=e^{9-x}
(\partial)/(\partial x)(10y+x)	\frac{\partial\:}{\partial\:x}(10y+x)
integral of 4(x^2+1)	\int\:4(x^{2}+1)dx
derivative of f(x)=(x^2-1)/2	derivative\:f(x)=\frac{x^{2}-1}{2}
integral of sec^2(x)-sin(x)	\int\:\sec^{2}(x)-\sin(x)dx
integral of 1/3 e^{3x}	\int\:\frac{1}{3}e^{3x}dx
integral from 0 to pi/2 of cos^5(6x)	\int\:_{0}^{\frac{π}{2}}\cos^{5}(6x)dx
integral of (sec^2(x))/(1+tan^2(x))	\int\:\frac{\sec^{2}(x)}{1+\tan^{2}(x)}dx
derivative of arctan(x+2sqrt(x)-2)	\frac{d}{dx}(\arctan(x)+2\sqrt{x}-2)
derivative of y=x^{15/16}	derivative\:y=x^{\frac{15}{16}}
integral of sqrt(2x)-1/(sqrt(2x))	\int\:\sqrt{2x}-\frac{1}{\sqrt{2x}}dx
integral of 1/(y+1)	\int\:\frac{1}{y+1}dy
integral of sin^3(4x)cos^9(4x)	\int\:\sin^{3}(4x)\cos^{9}(4x)dx
integral of (ln(x^{26}))/x	\int\:\frac{\ln(x^{26})}{x}dx
(\partial)/(\partial x)(240x^2-140y^2)	\frac{\partial\:}{\partial\:x}(240x^{2}-140y^{2})
laplacetransform tcos(5t)	laplacetransform\:t\cos(5t)
limit as x approaches-9 of-9	\lim\:_{x\to\:-9}(-9)
d/(dv)(uv)	\frac{d}{dv}(uv)
integral of (sqrt(x)-3/x)^2	\int\:(\sqrt{x}-\frac{3}{x})^{2}dx
integral of 3/(1-2x)	\int\:\frac{3}{1-2x}dx
integral of cos(2pix)	\int\:\cos(2πx)dx
(\partial)/(\partial z)(xysin(z))	\frac{\partial\:}{\partial\:z}(xy\sin(z))
(dy)/(dx)=(x/(2000))-(y/(5000)),y(0)=0	\frac{dy}{dx}=(\frac{x}{2000})-(\frac{y}{5000}),y(0)=0
limit as x approaches 5 of-((x+1)/(x-5))	\lim\:_{x\to\:5}(-(\frac{x+1}{x-5}))
integral of x/5	\int\:\frac{x}{5}dx
derivative of 5/(3x)	\frac{d}{dx}(\frac{5}{3x})
tangent of f(x)=((e^{2x}+1))/(e^x-2)	tangent\:f(x)=\frac{(e^{2x}+1)}{e^{x}-2}
tangent of x^4-3x^3+5	tangent\:x^{4}-3x^{3}+5
derivative of y=e^{8/9 x}	derivative\:y=e^{\frac{8}{9}x}
integral of t^2e^{-12t}	\int\:t^{2}e^{-12t}dt
integral of (x^2+x-6)/(x^2-4x+3)	\int\:\frac{x^{2}+x-6}{x^{2}-4x+3}dx
(\partial)/(\partial x)((4x+y)/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{4x+y}{x-y})
limit as x approaches-infinity of 3^{4x}	\lim\:_{x\to\:-\infty\:}(3^{4x})
integral from 0 to 0.5 of 5arccos(x)	\int\:_{0}^{0.5}5\arccos(x)dx
area y= 1/(x^2)+x,x=2,x=4	area\:y=\frac{1}{x^{2}}+x,x=2,x=4
limit as x approaches 0 of x^6sin(x)	\lim\:_{x\to\:0}(x^{6}\sin(x))
derivative of f(x)=e^x-2x	derivative\:f(x)=e^{x}-2x
derivative of (3x-1(x+2))	\frac{d}{dx}((3x-1)(x+2))
limit as x approaches 0+of 2-x	\lim\:_{x\to\:0+}(2-x)
y^'=y-8	y^{\prime\:}=y-8
integral from 0 to 1 of 7x^4e^{-x}	\int\:_{0}^{1}7x^{4}e^{-x}dx
integral of (21)/(21+e^x)	\int\:\frac{21}{21+e^{x}}dx
y^'=(3x^2+2x+1)/(y-2)	y^{\prime\:}=\frac{3x^{2}+2x+1}{y-2}
integral from 0 to 2 of x/(x+x^2)	\int\:_{0}^{2}\frac{x}{x+x^{2}}dx
integral of 9/(x^2)	\int\:\frac{9}{x^{2}}dx
inverse oflaplace 1/(10s)	inverselaplace\:\frac{1}{10s}
y^'=3y(5-y)	y^{\prime\:}=3y(5-y)
y^'=((2x))/(1+2y),y(2)=1	y^{\prime\:}=\frac{(2x)}{1+2y},y(2)=1
derivative of y=ln(x^2\sqrt[3]{5x+2})	derivative\:y=\ln(x^{2}\sqrt[3]{5x+2})
limit as x approaches 0 of ln(2)	\lim\:_{x\to\:0}(\ln(2))
sum from n=1 to infinity of 1/(n^2+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+1}
2xydx+(x^2+1)dy=0	2xydx+(x^{2}+1)dy=0
derivative of e^x-2x	\frac{d}{dx}(e^{x}-2x)
f(x)=sqrt(3-2x)	f(x)=\sqrt{3-2x}
derivative of sin(x^3-3x)	\frac{d}{dx}(\sin(x^{3}-3x))
derivative of x^{-1}-1/x	derivative\:x^{-1}-\frac{1}{x}
derivative of f(x)=xe^{2x}	derivative\:f(x)=xe^{2x}
integral of (x^5)/(x^6-6)	\int\:\frac{x^{5}}{x^{6}-6}dx
integral of (e^t)/(1+e^{2t)}	\int\:\frac{e^{t}}{1+e^{2t}}dt
limit as x approaches-5+of (\|x+5\|)/(x+5)	\lim\:_{x\to\:-5+}(\frac{\left\|x+5\right\|}{x+5})
derivative of sin^3(2x^2)	\frac{d}{dx}(\sin^{3}(2x^{2}))
integral of 4^x*e^{2x}	\int\:4^{x}\cdot\:e^{2x}dx
limit as x approaches 0 of x-10+5x	\lim\:_{x\to\:0}(x-10+5x)
derivative of 3a^{5x}	\frac{d}{dx}(3a^{5x})
(\partial)/(\partial x)(2yzln(1+x^2))	\frac{\partial\:}{\partial\:x}(2yz\ln(1+x^{2}))
derivative of 5xe^{-kx}	derivative\:5xe^{-kx}
derivative of arcsin(sqrt(x^2-4))	\frac{d}{dx}(\arcsin(\sqrt{x^{2}-4}))
y=e^{-2((x-146)-2((ln(19.52))/2))}	y=e^{-2((x-146)-2(\frac{\ln(19.52)}{2}))}
integral from 0 to 3 of (x-1)	\int\:_{0}^{3}(x-1)dx
integral of (3x^2-7x+4)	\int\:(3x^{2}-7x+4)dx
integral of (3x^39x^2-15)/(x^24x^4)	\int\:\frac{3x^{3}9x^{2}-15}{x^{2}4x^{4}}dx
derivative of arcsin(3x+y)	\frac{d}{dx}(\arcsin(3x+y))
derivative of ln(5x+3)	\frac{d}{dx}(\ln(5x+3))
integral of 4e^{-x}(e^{-3x}+1)	\int\:4e^{-x}(e^{-3x}+1)dx
derivative of (9x/(e^x))	\frac{d}{dx}(\frac{9x}{e^{x}})
derivative of f(x)=arccos(3x)	derivative\:f(x)=\arccos(3x)
derivative of arctan(x-sqrt(1+x^2))	\frac{d}{dx}(\arctan(x-\sqrt{1+x^{2}}))
(dy)/(dx)=x^2(1-y)	\frac{dy}{dx}=x^{2}(1-y)
integral of \sqrt[3]{x}+cos(3x)	\int\:\sqrt[3]{x}+\cos(3x)dx
(\partial)/(\partial y)(sqrt(2x^2y-5y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{2x^{2}y-5y^{2}})
integral of (cos(x))/((1+sin(x))^5)	\int\:\frac{\cos(x)}{(1+\sin(x))^{5}}dx
derivative of (e^{x^2}+4^2*(4x)^{3x})	\frac{d}{dx}((e^{x^{2}}+4)^{2}\cdot\:(4x)^{3x})
inverse oflaplace (16)/(s(s^2+16))	inverselaplace\:\frac{16}{s(s^{2}+16)}

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