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Popular Calculus Problems

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))
integral of 1/(cos(x)+2sin(x)+3)	\int\:\frac{1}{\cos(x)+2\sin(x)+3}dx
sum from n=2 to infinity of (ln(n^2))/n	\sum\:_{n=2}^{\infty\:}\frac{\ln(n^{2})}{n}
inverse oflaplace ((s^2+1))/(s+5)	inverselaplace\:\frac{(s^{2}+1)}{s+5}
integral from 0 to 4 of (2x+4)^{-1/2}	\int\:_{0}^{4}(2x+4)^{-\frac{1}{2}}dx
(\partial)/(\partial y)(xsin(y)sin(z))	\frac{\partial\:}{\partial\:y}(x\sin(y)\sin(z))
derivative of ln(sqrt((x+6/(x-6))))	\frac{d}{dx}(\ln(\sqrt{\frac{x+6}{x-6}}))
y^'=-(2xy)/(1+x^2)	y^{\prime\:}=-\frac{2xy}{1+x^{2}}
f(z)= 1/z	f(z)=\frac{1}{z}
integral of 25t^4e^{-t^5}	\int\:25t^{4}e^{-t^{5}}dt
limit as x approaches 13 of pi	\lim\:_{x\to\:13}(π)
derivative of 10x^{3/2}	\frac{d}{dx}(10x^{\frac{3}{2}})
integral from 1 to 2 of 8/(x^2-2x+2)	\int\:_{1}^{2}\frac{8}{x^{2}-2x+2}dx
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)
integral of e^{6x+9}	\int\:e^{6x+9}dx
(\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
limit as x approaches 1 of 3x^3-5x^2+x+5	\lim\:_{x\to\:1}(3x^{3}-5x^{2}+x+5)
derivative of-1/5 cos(5x)	\frac{d}{dx}(-\frac{1}{5}\cos(5x))
y^{''}-6y^'+13y=0,y(0)=0,y^'(0)=-3	y^{\prime\:\prime\:}-6y^{\prime\:}+13y=0,y(0)=0,y^{\prime\:}(0)=-3
yy^'-6e^x=0	yy^{\prime\:}-6e^{x}=0
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})
tangent of f(x)=(8x)/(x^2+1),(-1,-4)	tangent\:f(x)=\frac{8x}{x^{2}+1},(-1,-4)
integral from-2 to 0 of (x+2)^2	\int\:_{-2}^{0}(x+2)^{2}dx
derivative of x/(sqrt(x))	derivative\:\frac{x}{\sqrt{x}}
derivative of 2.6-3.15t^2+7.3t^3	derivative\:2.6-3.15t^{2}+7.3t^{3}
limit as x approaches 0 of sin(6x)	\lim\:_{x\to\:0}(\sin(6x))
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
integral of e^{(2x)/3}	\int\:e^{\frac{2x}{3}}dx
integral from 0 to 1 of (x^2)/(e^x)	\int\:_{0}^{1}\frac{x^{2}}{e^{x}}dx
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
area-x^2-2x+9,[-4,0]	area\:-x^{2}-2x+9,[-4,0]
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
integral from 0 to 3 of xe^{-2x}	\int\:_{0}^{3}xe^{-2x}dx
integral of (x^2)/9	\int\:\frac{x^{2}}{9}dx
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}})
integral of (x+21)/(x^2+12x+40)	\int\:\frac{x+21}{x^{2}+12x+40}dx
sum from n=0 to infinity of (n^3)/(3^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{3}}{3^{n}}
derivative of ((x^3/9)^2)	\frac{d}{dx}((\frac{x^{3}}{9})^{2})
(\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}))
y^{''}-2y^'=7t	y^{\prime\:\prime\:}-2y^{\prime\:}=7t
(\partial)/(\partial x)(x^{0.5}y^{0.5}z)	\frac{\partial\:}{\partial\:x}(x^{0.5}\cdot\:y^{0.5}\cdot\:z)
tangent of y=x^3-3x+3,(3,21)	tangent\:y=x^{3}-3x+3,(3,21)
integral from 0 to t of e^{-kt}	\int\:_{0}^{t}e^{-kt}dt
limit as x approaches pi/2 of (sec(x))/(sec(3x))	\lim\:_{x\to\:\frac{π}{2}}(\frac{\sec(x)}{\sec(3x)})
integral of (x^2-1)^3(2x)	\int\:(x^{2}-1)^{3}(2x)dx
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
integral of 1-x^2	\int\:1-x^{2}dx
tangent of f(x)=\sqrt[3]{x+2}+1,\at x=6	tangent\:f(x)=\sqrt[3]{x+2}+1,\at\:x=6
derivative of f(x)=6x+8	derivative\:f(x)=6x+8
derivative of arctan(sqrt(7x^2-1))	\frac{d}{dx}(\arctan(\sqrt{7x^{2}-1}))
derivative of e^{3-x}	derivative\:e^{3-x}
derivative of (3x-2^2(3-x^2)^2)	\frac{d}{dx}((3x-2)^{2}(3-x^{2})^{2})
derivative of y=(e^x+x)^5	derivative\:y=(e^{x}+x)^{5}
derivative of f(x)=2^{4x}+4x^2	derivative\:f(x)=2^{4x}+4x^{2}
y^'+xy=xy^3	y^{\prime\:}+xy=xy^{3}
implicit (dy)/(dx),5xy=8	implicit\:\frac{dy}{dx},5xy=8
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}
integral of (sqrt(x)-1)^2(sqrt(x)+1)^2	\int\:(\sqrt{x}-1)^{2}(\sqrt{x}+1)^{2}dx
integral of 5-x	\int\:5-xdx
derivative of-3cot(2xsec(2x))	\frac{d}{dx}(-3\cot(2x)\sec(2x))
integral of x^2+8e^x+C	\int\:x^{2}+8e^{x}+Cdx
y^{''}+3y^'+2y=e^x+e^{2x}	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=e^{x}+e^{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
(x+1)y^'+xy=0	(x+1)y^{\prime\:}+xy=0
derivative of (2x^2-1/(3x^3-1))	\frac{d}{dx}(\frac{2x^{2}-1}{3x^{3}-1})
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
integral of (e^{2x}(1+2xln(x)))/(4x)	\int\:\frac{e^{2x}(1+2x\ln(x))}{4x}dx
integral of x/((4-x^2)^2)	\int\:\frac{x}{(4-x^{2})^{2}}dx
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
laplacetransform f(t)=4t^2-5sin(3t)	laplacetransform\:f(t)=4t^{2}-5\sin(3t)
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

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