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Popular Calculus Problems

integral from 0 to pi of xcos(2x)	\int\:_{0}^{π}x\cos(2x)dx
inverse oflaplace (32)/((s^2+4^2)(s+4)^2)	inverselaplace\:\frac{32}{(s^{2}+4^{2})(s+4)^{2}}
limit as x approaches 3 of 8x+2	\lim\:_{x\to\:3}(8x+2)
integral of 1/4 e^{sqrt(x-1)}	\int\:\frac{1}{4}e^{\sqrt{x-1}}dx
derivative of 3e^x+4/(\sqrt[3]{x)}	derivative\:3e^{x}+\frac{4}{\sqrt[3]{x}}
derivative of 1/(10-x)	\frac{d}{dx}(\frac{1}{10-x})
integral of (ye^{xy})	\int\:(ye^{xy})dx
integral of 1.8^{0.045x}	\int\:1.8^{0.045x}dx
integral of ((x^2))/((x+3)^3)	\int\:\frac{(x^{2})}{(x+3)^{3}}dx
inverse oflaplace ((s-5))/(s^2+4s+20)	inverselaplace\:\frac{(s-5)}{s^{2}+4s+20}
(\partial)/(\partial x)((7xy)/(x^2+y^4))	\frac{\partial\:}{\partial\:x}(\frac{7xy}{x^{2}+y^{4}})
(\partial)/(\partial z)(-3z)	\frac{\partial\:}{\partial\:z}(-3z)
x^'+3x=0	x^{\prime\:}+3x=0
integral of 13tan^3(x)sec(x)	\int\:13\tan^{3}(x)\sec(x)dx
(dy)/(dt)+(3t)/(t^2+1)y=(6t)/(t^2+1)	\frac{dy}{dt}+\frac{3t}{t^{2}+1}y=\frac{6t}{t^{2}+1}
area (x-1)^3,x-1,0,1	area\:(x-1)^{3},x-1,0,1
limit as x approaches 0 of (sec(x))/x	\lim\:_{x\to\:0}(\frac{\sec(x)}{x})
area x^2+2,2x+5	area\:x^{2}+2,2x+5
x^2y^{''}+2xy^'-12y=0	x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}-12y=0
(\partial)/(\partial x)(42x^5y^6-30x^4y^5)	\frac{\partial\:}{\partial\:x}(42x^{5}y^{6}-30x^{4}y^{5})
x^2y^{''}-5xy^'-7y=0	x^{2}y^{\prime\:\prime\:}-5xy^{\prime\:}-7y=0
derivative of f(x)=e^{-6x}	derivative\:f(x)=e^{-6x}
integral of e^{1.2x}	\int\:e^{1.2x}dx
derivative of 4-sqrt(x+16)	derivative\:4-\sqrt{x+16}
derivative of 5pi^6	derivative\:5π^{6}
limit as x approaches 0-of arctan(ln(x))	\lim\:_{x\to\:0-}(\arctan(\ln(x)))
integral of x^{7/6}	\int\:x^{\frac{7}{6}}dx
integral of (x^2+8x-4)/(x^3-4x)	\int\:\frac{x^{2}+8x-4}{x^{3}-4x}dx
derivative of (x^2-4/(x+0.5))	\frac{d}{dx}(\frac{x^{2}-4}{x+0.5})
limit as y approaches 0 of ax^2+bx^3	\lim\:_{y\to\:0}(ax^{2}+bx^{3})
derivative of f(x)=2e^x(cos(x)-sin(x))	derivative\:f(x)=2e^{x}(\cos(x)-\sin(x))
slope ofintercept (3,4),(5,-4)	slopeintercept\:(3,4),(5,-4)
integral of (5e^{2x})/(e^{2x)+11e^x+24}	\int\:\frac{5e^{2x}}{e^{2x}+11e^{x}+24}dx
derivative of x^2+5x+4	\frac{d}{dx}(x^{2}+5x+4)
derivative of 9.75+1.5x^3	\frac{d}{dx}(9.75+1.5x^{3})
integral of 1-cos(4x)	\int\:1-\cos(4x)dx
derivative of 2e^{-2x}x-2e^{-2x}x^2	\frac{d}{dx}(2e^{-2x}x-2e^{-2x}x^{2})
(sqrt(4-x^2))^'	(\sqrt{4-x^{2}})^{\prime\:}
integral of-4sqrt(x)e^{sqrt(x)}	\int\:-4\sqrt{x}e^{\sqrt{x}}dx
normal of f(x)=(x+2)sqrt(2x-3),\at x=2	normal\:f(x)=(x+2)\sqrt{2x-3},\at\:x=2
area y= 1/x ,y=x,x=3	area\:y=\frac{1}{x},y=x,x=3
derivative of-(4x/(x^2+1))	\frac{d}{dx}(-\frac{4x}{x^{2}+1})
(arccos(x))^'	(\arccos(x))^{\prime\:}
integral of (ln(t))/(t^2)	\int\:\frac{\ln(t)}{t^{2}}dt
integral of ln(x^2+15x+44)	\int\:\ln(x^{2}+15x+44)dx
inverse oflaplace (3^2)/((s+3)^2)*1/s	inverselaplace\:\frac{3^{2}}{(s+3)^{2}}\cdot\:\frac{1}{s}
integral of (sqrt(1-w))/(sqrt(w))	\int\:\frac{\sqrt{1-w}}{\sqrt{w}}dw
(\partial)/(\partial v)(2sin(u)cos(v))	\frac{\partial\:}{\partial\:v}(2\sin(u)\cos(v))
derivative of y=(5x^2+8x+4)/(sqrt(x))	derivative\:y=\frac{5x^{2}+8x+4}{\sqrt{x}}
limit as x approaches 2 of sqrt(x^2+5)	\lim\:_{x\to\:2}(\sqrt{x^{2}+5})
derivative of (4x)^{2x}	derivative\:(4x)^{2x}
derivative of x^2+4x+4	\frac{d}{dx}(x^{2}+4x+4)
integral of x3^x	\int\:x3^{x}dx
derivative of (csc(x)/(cot(x)))	\frac{d}{dx}(\frac{\csc(x)}{\cot(x)})
integral of 1/(cos^2(6x))	\int\:\frac{1}{\cos^{2}(6x)}dx
(\partial)/(\partial y)((x^2+y)(x-y^2))	\frac{\partial\:}{\partial\:y}((x^{2}+y)(x-y^{2}))
derivative of 7^{sqrt(x)}	\frac{d}{dx}(7^{\sqrt{x}})
derivative of y=ln(3x+1)e^{x^2+4}	derivative\:y=\ln(3x+1)e^{x^{2}+4}
integral of (4x^2-3x+2)/(4x^2-4x+3)	\int\:\frac{4x^{2}-3x+2}{4x^{2}-4x+3}dx
integral from 1 to 2 of (e^{1/x})/(x^2)	\int\:_{1}^{2}\frac{e^{\frac{1}{x}}}{x^{2}}dx
factor 2cos(x)+cos^2(x)	factor\:2\cos(x)+\cos^{2}(x)
y^{''}+3y^'+2y=6	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=6
area f(x)=cos(x),0,2pi	area\:f(x)=\cos(x),0,2π
integral of (3cos(x))/(sin^2(x)+sin(x))	\int\:\frac{3\cos(x)}{\sin^{2}(x)+\sin(x)}dx
sum from n=3 to infinity of n/(e^{3n)}	\sum\:_{n=3}^{\infty\:}\frac{n}{e^{3n}}
derivative of (x^3/(x^2-4))	\frac{d}{dx}(\frac{x^{3}}{x^{2}-4})
area y=x^2-7x+6,x=2,x=6	area\:y=x^{2}-7x+6,x=2,x=6
limit as x approaches-5 of (1/5+1/x)/(5+x)	\lim\:_{x\to\:-5}(\frac{\frac{1}{5}+\frac{1}{x}}{5+x})
limit as x approaches 1 of 1/((1-x))	\lim\:_{x\to\:1}(\frac{1}{(1-x)})
derivative of 7log_{7}(x)	derivative\:7\log_{7}(x)
derivative of f(x)=e^{6x}	derivative\:f(x)=e^{6x}
integral of cos(2x)cos(3x)	\int\:\cos(2x)\cos(3x)dx
limit as x approaches 3 of x/((x-3)^2)	\lim\:_{x\to\:3}(\frac{x}{(x-3)^{2}})
derivative of ln(x^2-6x+1)	\frac{d}{dx}(\ln(x^{2}-6x+1))
laplacetransform 3te^{-5t}	laplacetransform\:3te^{-5t}
integral of (5x+4y)	\int\:(5x+4y)dx
integral of sqrt((9+x)/(9-x))	\int\:\sqrt{\frac{9+x}{9-x}}dx
(3x+2sqrt(3x))^'	(3x+2\sqrt{3x})^{\prime\:}
limit as x approaches infinity of 0*x	\lim\:_{x\to\:\infty\:}(0\cdot\:x)
integral of tan(x)sec^{3/2}(x)	\int\:\tan(x)\sec^{\frac{3}{2}}(x)dx
d/(dθ)(cos(4θ))	\frac{d}{dθ}(\cos(4θ))
derivative of x(x^2-3)	\frac{d}{dx}(x(x^{2}-3))
area x^2+3x-2,-x^2-3x+6	area\:x^{2}+3x-2,-x^{2}-3x+6
derivative of ln(x/(4x^2+x))	derivative\:\ln(\frac{x}{4x^{2}+x})
derivative of 1/2*\sqrt[3]{x}	\frac{d}{dx}(\frac{1}{2}\cdot\:\sqrt[3]{x})
derivative of ((e^x-1)/x)	\frac{d}{dx}(\frac{(e^{x}-1)}{x})
derivative of e^{sin^2(x})	\frac{d}{dx}(e^{\sin^{2}(x)})
area y= 2/x ,y=8x,y= 1/2 x	area\:y=\frac{2}{x},y=8x,y=\frac{1}{2}x
derivative of 3/(4(2x-5^8))	\frac{d}{dx}(\frac{3}{4(2x-5)^{8}})
limit as x approaches-infinity of (sqrt(x^2+8x))/(8x+1)	\lim\:_{x\to\:-\infty\:}(\frac{\sqrt{x^{2}+8x}}{8x+1})
derivative of f(x)=2000(x^2+5)^{1/3}	derivative\:f(x)=2000(x^{2}+5)^{\frac{1}{3}}
integral from 0 to 2 of e^{-x^2}	\int\:_{0}^{2}e^{-x^{2}}dx
derivative of 4x^3-10x^2	\frac{d}{dx}(4x^{3}-10x^{2})
(4x^2)^'	(4x^{2})^{\prime\:}
(\partial)/(\partial x)(e^{-(x-y)^2})	\frac{\partial\:}{\partial\:x}(e^{-(x-y)^{2}})
derivative of sqrt(15x)	derivative\:\sqrt{15x}
integral of ((x^2-2x-1))/(sqrt(x))	\int\:\frac{(x^{2}-2x-1)}{\sqrt{x}}dx
derivative of 5x^2sqrt(25-x^2)	derivative\:5x^{2}\sqrt{25-x^{2}}
integral from 0 to 5 of (5+3x)^{-1}	\int\:_{0}^{5}(5+3x)^{-1}dx
limit as x approaches 9-of (x-9)/(x-9)	\lim\:_{x\to\:9-}(\frac{x-9}{x-9})

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