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Popular Calculus Problems

integral from 0 to 1 of \sqrt[3]{x}-x^3	\int\:_{0}^{1}\sqrt[3]{x}-x^{3}dx
integral from 0 to 1 of sin(pit)	\int\:_{0}^{1}\sin(πt)dt
derivative of-4x^3+4x	\frac{d}{dx}(-4x^{3}+4x)
integral of c(x)	\int\:c(x)dx
derivative of h(x)=[(x+1)/(x-1)]^3	derivative\:h(x)=[\frac{x+1}{x-1}]^{3}
(\partial)/(\partial x)((y/z)^{1/x})	\frac{\partial\:}{\partial\:x}((\frac{y}{z})^{\frac{1}{x}})
y^{''}+3y=48x^2e^{3x}	y^{\prime\:\prime\:}+3y=48x^{2}e^{3x}
derivative of f(x)=x^{-4}	derivative\:f(x)=x^{-4}
(\partial)/(\partial x)(x+y+x^3+y^2)	\frac{\partial\:}{\partial\:x}(x+y+x^{3}+y^{2})
derivative of x^3sin(7x)	derivative\:x^{3}\sin(7x)
derivative of sqrt(6+7x)	\frac{d}{dx}(\sqrt{6+7x})
taylor e^{3x},0	taylor\:e^{3x},0
integral of x^2(5x^2+x)^2	\int\:x^{2}(5x^{2}+x)^{2}dx
(\partial)/(\partial h)(1/2 (a+b)h)	\frac{\partial\:}{\partial\:h}(\frac{1}{2}(a+b)h)
derivative of 2/(x^{1/3}-2)	\frac{d}{dx}(\frac{2}{x^{\frac{1}{3}}}-2)
y^{''}-2y^'+5y=5,y(0)=2,y^'(0)=1	y^{\prime\:\prime\:}-2y^{\prime\:}+5y=5,y(0)=2,y^{\prime\:}(0)=1
tangent of f(x)=((x-3)/(x+1))^2,\at x=0	tangent\:f(x)=(\frac{x-3}{x+1})^{2},\at\:x=0
integral of ye^{3y}	\int\:ye^{3y}dy
integral of (sin(x))/3	\int\:\frac{\sin(x)}{3}dx
integral from 1 to 2 of (x^2-4)	\int\:_{1}^{2}(x^{2}-4)dx
integral of 2cos^2(t)sin^2(t)	\int\:2\cos^{2}(t)\sin^{2}(t)dt
tangent of f(x)=x^2+3x+5,(1,9)	tangent\:f(x)=x^{2}+3x+5,(1,9)
limit as x approaches 2+of 1/(\|2-x\|)	\lim\:_{x\to\:2+}(\frac{1}{\left\|2-x\right\|})
derivative of 1/(x^2+a^2)	\frac{d}{dx}(\frac{1}{x^{2}+a^{2}})
integral from 0 to pi/6 of sin^4(6x)	\int\:_{0}^{\frac{π}{6}}\sin^{4}(6x)dx
inverse oflaplace (10)/((s)(s^2+8s+25))	inverselaplace\:\frac{10}{(s)(s^{2}+8s+25)}
integral of ((x^2+x-10))/((2x-3)(x^2+4))	\int\:\frac{(x^{2}+x-10)}{(2x-3)(x^{2}+4)}dx
derivative of-6sin(3x)	\frac{d}{dx}(-6\sin(3x))
sum from n=2 to infinity of (ln(n^2))/n	\sum\:_{n=2}^{\infty\:}\frac{\ln(n^{2})}{n}
(\partial)/(\partial y)(xsin(y)sin(z))	\frac{\partial\:}{\partial\:y}(x\sin(y)\sin(z))
f(z)= 1/z	f(z)=\frac{1}{z}
derivative of (4x/(x^2+4))	\frac{d}{dx}(\frac{4x}{x^{2}+4})
integral of (x^3)/(sqrt(9-x^2))	\int\:\frac{x^{3}}{\sqrt{9-x^{2}}}dx
(\partial)/(\partial y)(4x^2+y^2)	\frac{\partial\:}{\partial\:y}(4x^{2}+y^{2})
(\partial)/(\partial y)(sqrt(8-2x^2+y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{8-2x^{2}+y^{2}})
derivative of f(x)=x^2(x^2+1)	derivative\:f(x)=x^{2}(x^{2}+1)
(\partial)/(\partial y)(xe^{-x^2-y^2})	\frac{\partial\:}{\partial\:y}(xe^{-x^{2}-y^{2}})
integral from 0 to 4 of xsqrt(16-x^2)	\int\:_{0}^{4}x\sqrt{16-x^{2}}dx
integral of (1-t)/t	\int\:\frac{1-t}{t}dt
y^{''}-6y^'+13y=0,y(0)=0,y^'(0)=-3	y^{\prime\:\prime\:}-6y^{\prime\:}+13y=0,y(0)=0,y^{\prime\:}(0)=-3
derivative of \sqrt[3]{sin^2(2x})	\frac{d}{dx}(\sqrt[3]{\sin^{2}(2x)})
integral of sec(1)	\int\:\sec(1)dx
limit as x approaches x/4 of (sin(x))/x	\lim\:_{x\to\:\frac{x}{4}}(\frac{\sin(x)}{x})
integral of pi/2 pi/(32)sec(2θ)tan(2θ)	\int\:\frac{π}{2}\frac{π}{32}\sec(2θ)\tan(2θ)dθ
(\partial)/(\partial y)(10e^xsin(y)z^3)	\frac{\partial\:}{\partial\:y}(10e^{x}\sin(y)z^{3})
f(θ)=3cos(θ)	f(θ)=3\cos(θ)
integral of 1/(cos^2(t)sqrt(1+tan(t)))	\int\:\frac{1}{\cos^{2}(t)\sqrt{1+\tan(t)}}dt
limit as x approaches 2 of 5/((x-5)^2)	\lim\:_{x\to\:2}(\frac{5}{(x-5)^{2}})
3y^{''}-6y^'+6y=0	3y^{\prime\:\prime\:}-6y^{\prime\:}+6y=0
integral of (4x^2)/(\sqrt[3]{x^3-6)}	\int\:\frac{4x^{2}}{\sqrt[3]{x^{3}-6}}dx
derivative of f(x)=arcsin(8t)	derivative\:f(x)=\arcsin(8t)
derivative of 1/4 e^x+e^{-x}	\frac{d}{dx}(\frac{1}{4}e^{x}+e^{-x})
derivative of (dy/(dx))+4y=0	\frac{d}{dx}(\frac{dy}{dx})+4y=0
integral of (sin^2(x))/(sqrt(x))	\int\:\frac{\sin^{2}(x)}{\sqrt{x}}dx
integral of 1/(2x^3+2x^2)	\int\:\frac{1}{2x^{3}+2x^{2}}dx
derivative of arcsin(3x^2)	\frac{d}{dx}(\arcsin(3x^{2}))
derivative of-2y	derivative\:-2y
tangent of f(x)=5e^x+x,(0,5)	tangent\:f(x)=5e^{x}+x,(0,5)
limit as x approaches b of (x-b)/(sqrt(x)-\sqrt{b)}	\lim\:_{x\to\:b}(\frac{x-b}{\sqrt{x}-\sqrt{b}})
(\partial)/(\partial y)(1/y)	\frac{\partial\:}{\partial\:y}(\frac{1}{y})
limit as x approaches 1 of cos(1/(x-1))	\lim\:_{x\to\:1}(\cos(\frac{1}{x-1}))
tangent of y=x^3-3x+3,(3,21)	tangent\:y=x^{3}-3x+3,(3,21)
limit as x approaches pi/2 of (sec(x))/(sec(3x))	\lim\:_{x\to\:\frac{π}{2}}(\frac{\sec(x)}{\sec(3x)})
tangent of f(x)=3+4x^2-2x^3,\at x=a	tangent\:f(x)=3+4x^{2}-2x^{3},\at\:x=a
(y+4)y^'=2xy+4y,y(2)=1	(y+4)y^{\prime\:}=2xy+4y,y(2)=1
integral of (1+30w)sqrt(w)	\int\:(1+30w)\sqrt{w}dw
derivative of f(x)=6x+8	derivative\:f(x)=6x+8
derivative of e^{3-x}	derivative\:e^{3-x}
derivative of f(x)=2^{4x}+4x^2	derivative\:f(x)=2^{4x}+4x^{2}
y^'+xy=xy^3	y^{\prime\:}+xy=xy^{3}
limit as x approaches 0 of x/(x+7)	\lim\:_{x\to\:0}(\frac{x}{x+7})
y^'=1+sqrt(y-2x+3)	y^{\prime\:}=1+\sqrt{y-2x+3}
derivative of-3cot(2xsec(2x))	\frac{d}{dx}(-3\cot(2x)\sec(2x))
integral of 1/(3x+2)	\int\:\frac{1}{3x+2}dx
integral from 0 to 2 of (x-3)^2-(x-1)^2	\int\:_{0}^{2}(x-3)^{2}-(x-1)^{2}dx
integral of e^{-x}sin^2(x)	\int\:e^{-x}\sin^{2}(x)dx
(dx}{dt}=\frac{4x)/t ,x(1)=1	\frac{dx}{dt}=\frac{4x}{t},x(1)=1
tangent of (4x)/(x+1)	tangent\:\frac{4x}{x+1}
integral from 1 to 1.5 of (1/8+3/8 x)	\int\:_{1}^{1.5}(\frac{1}{8}+\frac{3}{8}x)dx
limit as x approaches-infinity of x^1	\lim\:_{x\to\:-\infty\:}(x^{1})
integral from 0 to pi of 11sin^2(2x)	\int\:_{0}^{π}11\sin^{2}(2x)dx
derivative of y=ln(8x^2-7x+9)	derivative\:y=\ln(8x^{2}-7x+9)
derivative of f(t)=e^{9tsin(2t)}	derivative\:f(t)=e^{9t\sin(2t)}
derivative of (x^2)/(x+8)	derivative\:\frac{x^{2}}{x+8}
integral of 3sec^{-2}(xta)n^3x	\int\:3\sec^{-2}(xta)n^{3}xdx
limit as x approaches 9 of 2x^2-3	\lim\:_{x\to\:9}(2x^{2}-3)
(\partial)/(\partial x)(sin(x^3)+3xy)	\frac{\partial\:}{\partial\:x}(\sin(x^{3})+3xy)
laplacetransform t^2cos(4t)	laplacetransform\:t^{2}\cos(4t)
integral of ye	\int\:yedy
integral of cos(x)sqrt(9-sin^2(x))	\int\:\cos(x)\sqrt{9-\sin^{2}(x)}dx
7xy^'-2y=(-x^2)/(y^6)	7xy^{\prime\:}-2y=\frac{-x^{2}}{y^{6}}
derivative of 5x^2+3x	\frac{d}{dx}(5x^{2}+3x)
y^{''}-2y^'+y=12te^t+2e^t+t-4	y^{\prime\:\prime\:}-2y^{\prime\:}+y=12te^{t}+2e^{t}+t-4
derivative of 8x-2x^2	\frac{d}{dx}(8x-2x^{2})
limit as x approaches-6 of sqrt(36-x^2)	\lim\:_{x\to\:-6}(\sqrt{36-x^{2}})
integral of cos(3x)cos(x)	\int\:\cos(3x)\cos(x)dx
sum from n=1 to infinity of 1/(4n)	\sum\:_{n=1}^{\infty\:}\frac{1}{4n}
derivative of (t-2)^2	derivative\:(t-2)^{2}
limit as x approaches c of (x-c)/(2x-2c)	\lim\:_{x\to\:c}(\frac{x-c}{2x-2c})
integral of-2/t	\int\:-\frac{2}{t}dt

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