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Popular Calculus Problems

limit as x approaches 0 of ((e^{3x}-1))/(sin(5x))	\lim\:_{x\to\:0}(\frac{(e^{3x}-1)}{\sin(5x)})
integral of cos^3(x)sin^3(x)	\int\:\cos^{3}(x)\sin^{3}(x)dx
y^{''}-81y=0	y^{\prime\:\prime\:}-81y=0
derivative of e^{2x+4}	derivative\:e^{2x+4}
derivative of (2x+3)/(3x-2)	derivative\:\frac{2x+3}{3x-2}
integral of (\sqrt[3]{2x+1})	\int\:(\sqrt[3]{2x+1})dx
limit as h approaches+0 of-(5h)/(x(x+h))	\lim\:_{h\to\:+0}(-\frac{5h}{x(x+h)})
derivative of-3/(1-3x)	\frac{d}{dx}(-\frac{3}{1-3x})
integral of (6000)/(6x+70)	\int\:\frac{6000}{6x+70}dx
derivative of y= x/(x+b/x)	derivative\:y=\frac{x}{x+\frac{b}{x}}
taylor 1/((1+x)^3),0	taylor\:\frac{1}{(1+x)^{3}},0
inverse oflaplace 3/(s^2+9)	inverselaplace\:\frac{3}{s^{2}+9}
tangent of h(x)= 9/x ,\at x=2	tangent\:h(x)=\frac{9}{x},\at\:x=2
taylor e^{-5x-3},5	taylor\:e^{-5x-3},5
derivative of f(x)=(x^2-10x)*(x-14)	derivative\:f(x)=(x^{2}-10x)\cdot\:(x-14)
integral of \sqrt[3]{64x^5}	\int\:\sqrt[3]{64x^{5}}dx
integral from-18 to 32 of 1/(sqrt(\|2x\|))	\int\:_{-18}^{32}\frac{1}{\sqrt{\left\|2x\right\|}}dx
inverse oflaplace 3-2/(s-1)	inverselaplace\:3-\frac{2}{s-1}
area x^2-6x+9,x^2-x+6,[0,5]	area\:x^{2}-6x+9,x^{2}-x+6,[0,5]
t(dy)/(dt)=t^3+6t^3y	t\frac{dy}{dt}=t^{3}+6t^{3}y
limit as x approaches 0+of x(12)	\lim\:_{x\to\:0+}(x(12))
integral from a to sqrt(3a of)x	\int\:_{a}^{\sqrt{3a}}xdx
area x-2,sqrt(x),0,4	area\:x-2,\sqrt{x},0,4
limit as x approaches-7 of (4x+28)/(x+7)	\lim\:_{x\to\:-7}(\frac{4x+28}{x+7})
integral of sec^6(x)tan^2(x)	\int\:\sec^{6}(x)\tan^{2}(x)dx
limit as x approaches 2 of (x^x-4)/(x-2)	\lim\:_{x\to\:2}(\frac{x^{x}-4}{x-2})
integral of 1/(x*(x-1))	\int\:\frac{1}{x\cdot\:(x-1)}dx
(\partial)/(\partial x)((12x)/(sqrt(y+6)))	\frac{\partial\:}{\partial\:x}(\frac{12x}{\sqrt{y+6}})
derivative of (ln(8x))/(8x)	derivative\:\frac{\ln(8x)}{8x}
integral of 3/(e^{sqrt(x))}	\int\:\frac{3}{e^{\sqrt{x}}}dx
derivative of \sqrt[3]{x}(x^2+4)	\frac{d}{dx}(\sqrt[3]{x}(x^{2}+4))
integral of e^{-v}	\int\:e^{-v}dv
slope of (2,3),(4,-4)	slope\:(2,3),(4,-4)
taylor x*e^{-x+1},1	taylor\:x\cdot\:e^{-x+1},1
integral of 1/(2x^2-2x+1)	\int\:\frac{1}{2x^{2}-2x+1}dx
integral of (5e^x)	\int\:(5e^{x})dx
tangent of f(x)= 1/(x-2),\at x=7	tangent\:f(x)=\frac{1}{x-2},\at\:x=7
integral of x/(sqrt(36x^2-1))	\int\:\frac{x}{\sqrt{36x^{2}-1}}dx
derivative of f(x)=6e^x+2/(\sqrt[3]{x)}	derivative\:f(x)=6e^{x}+\frac{2}{\sqrt[3]{x}}
(\partial)/(\partial x)(ln(x^7+y^2))	\frac{\partial\:}{\partial\:x}(\ln(x^{7}+y^{2}))
integral of (4x)/(1+x^2)	\int\:\frac{4x}{1+x^{2}}dx
limit as x approaches 1 of x/(x^2-2x)	\lim\:_{x\to\:1}(\frac{x}{x^{2}-2x})
derivative of f(x)=x^3-3x+2	derivative\:f(x)=x^{3}-3x+2
derivative of 1/(sqrt(x^{15)})	\frac{d}{dx}(\frac{1}{\sqrt{x^{15}}})
area 1/(14x^2),x, x/4	area\:\frac{1}{14x^{2}},x,\frac{x}{4}
integral of x^2-x^3	\int\:x^{2}-x^{3}dx
integral from 0 to 1 of 1/(\sqrt[3]{x)}	\int\:_{0}^{1}\frac{1}{\sqrt[3]{x}}dx
integral from 0 to 25 of (-6sqrt(x))	\int\:_{0}^{25}(-6\sqrt{x})dx
limit as x approaches 2 of x^3-5x^2+1	\lim\:_{x\to\:2}(x^{3}-5x^{2}+1)
integral from 0 to 2 of (x+y)	\int\:_{0}^{2}(x+y)dy
tangent of 1/(sqrt(8x))	tangent\:\frac{1}{\sqrt{8x}}
derivative of ln(sqrt(e^{-2x)+cos(x}))	\frac{d}{dx}(\ln(\sqrt{e^{-2x}+\cos(x)}))
integral from 0 to 3 of (x/3+5)	\int\:_{0}^{3}(\frac{x}{3}+5)dx
derivative of (5-x^2/(5+x^2))	\frac{d}{dx}(\frac{5-x^{2}}{5+x^{2}})
(\partial)/(\partial x)(1/6 x^3)	\frac{\partial\:}{\partial\:x}(\frac{1}{6}x^{3})
tangent of f(x)=2x^2+3x-2,(-1,-3)	tangent\:f(x)=2x^{2}+3x-2,(-1,-3)
integral of 1/(sqrt(4-x^2))	\int\:\frac{1}{\sqrt{4-x^{2}}}dx
9xy^'+y=90x	9xy^{\prime\:}+y=90x
g(x)=x^{-5/3}-sqrt(x)+e^{40}	g(x)=x^{-\frac{5}{3}}-\sqrt{x}+e^{40}
integral of (10)/(cos(θ)-1)	\int\:\frac{10}{\cos(θ)-1}dθ
integral of sqrt(5+4x^2)	\int\:\sqrt{5+4x^{2}}dx
derivative of ln(2^x-4)	derivative\:\ln(2^{x}-4)
(\partial)/(\partial y)(3cos(x)-sin(x)y)	\frac{\partial\:}{\partial\:y}(3\cos(x)-\sin(x)y)
area y=(25-4x^2)^2,x=-5/2 ,x= 5/2	area\:y=(25-4x^{2})^{2},x=-\frac{5}{2},x=\frac{5}{2}
integral of (5x+3)/(x^2+1)	\int\:\frac{5x+3}{x^{2}+1}dx
sum from n=1 to infinity of 19^nx^nn!	\sum\:_{n=1}^{\infty\:}19^{n}x^{n}n!
limit as x approaches-2+of (-6x)/(x+2)	\lim\:_{x\to\:-2+}(\frac{-6x}{x+2})
integral of x/(x^4+2x^2+1)	\int\:\frac{x}{x^{4}+2x^{2}+1}dx
(\partial)/(\partial x)(ln(x^4+y^4)-z)	\frac{\partial\:}{\partial\:x}(\ln(x^{4}+y^{4})-z)
(\partial)/(\partial x)(3/(x^3))	\frac{\partial\:}{\partial\:x}(\frac{3}{x^{3}})
derivative of (e^x/(8x^2+7))	\frac{d}{dx}(\frac{e^{x}}{8x^{2}+7})
derivative of f(x)=x(1/x)	derivative\:f(x)=x(\frac{1}{x})
integral of 15	\int\:15dx
derivative of 4x^3+6x^2-5	\frac{d}{dx}(4x^{3}+6x^{2}-5)
(\partial)/(\partial x)(x^4-4x^3y+6x^2y^2)	\frac{\partial\:}{\partial\:x}(x^{4}-4x^{3}y+6x^{2}y^{2})
slope of-3x^2-2xy+3y^3=57,(-4,3)	slope\:-3x^{2}-2xy+3y^{3}=57,(-4,3)
integral of 1/(1-sin(1/2 x))	\int\:\frac{1}{1-\sin(\frac{1}{2}x)}dx
t^2y^{''}+ty^'+4y=0	t^{2}y^{\prime\:\prime\:}+ty^{\prime\:}+4y=0
integral of 3x^3cos(5x)	\int\:3x^{3}\cos(5x)dx
limit as x approaches 5 of sqrt(x^2+11)	\lim\:_{x\to\:5}(\sqrt{x^{2}+11})
limit as x approaches+(-3)-of 2x^2-6	\lim\:_{x\to\:+(-3)-}(2x^{2}-6)
integral of (sqrt(100-x^2))/x	\int\:\frac{\sqrt{100-x^{2}}}{x}dx
integral from pi/2 to pi of 5sin(x)	\int\:_{\frac{π}{2}}^{π}5\sin(x)dx
integral of \sqrt[3]{at}	\int\:\sqrt[3]{at}dt
(2y)^'	(2y)^{\prime\:}
integral of 1/((x^2+1)(x^2+4))	\int\:\frac{1}{(x^{2}+1)(x^{2}+4)}dx
integral of x/(8x-7)	\int\:\frac{x}{8x-7}dx
(\partial)/(\partial z)(6x^{y/z})	\frac{\partial\:}{\partial\:z}(6x^{\frac{y}{z}})
inverse oflaplace 1/(s+3)-1/(s+4)	inverselaplace\:\frac{1}{s+3}-\frac{1}{s+4}
(\partial}{\partial s}(\frac{(2r+s))/t)	\frac{\partial\:}{\partial\:s}(\frac{(2r+s)}{t})
d/(dy)(xsin(xy))	\frac{d}{dy}(x\sin(xy))
limit as x approaches 1 of 1/(x-2)	\lim\:_{x\to\:1}(\frac{1}{x-2})
(\partial)/(\partial x)(3ysin(7y^2x))	\frac{\partial\:}{\partial\:x}(3y\sin(7y^{2}x))
derivative of (2x+8x^2)/((1+8x)^2)	derivative\:\frac{2x+8x^{2}}{(1+8x)^{2}}
integral from 0 to 1/3 of 4/(1+9x^2)	\int\:_{0}^{\frac{1}{3}}\frac{4}{1+9x^{2}}dx
tangent of y=x^3-2x^2+5	tangent\:y=x^{3}-2x^{2}+5
integral of rln(r)	\int\:r\ln(r)dr
limit as x approaches 1 of (x^8-1)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{8}-1}{x-1})
sum from n=1 to infinity}((3^{n-1 of))/(9^n)	\sum\:_{n=1}^{\infty\:}\frac{(3^{n-1})}{9^{n}}
integral from 1 to 2 of 2xsqrt(x^2+1)	\int\:_{1}^{2}2x\sqrt{x^{2}+1}dx

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