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Popular Calculus Problems

integral of 1/(sin^2(y))	\int\:\frac{1}{\sin^{2}(y)}dy
integral of sqrt(121-x^2)	\int\:\sqrt{121-x^{2}}dx
inverse oflaplace sin(6(t-pi/6))	inverselaplace\:\sin(6(t-\frac{π}{6}))
limit as x approaches-infinity of 2x^5	\lim\:_{x\to\:-\infty\:}(2x^{5})
tangent of y= 1/(sqrt(x)),\at x=a	tangent\:y=\frac{1}{\sqrt{x}},\at\:x=a
(\partial)/(\partial x)(4tan(xy))	\frac{\partial\:}{\partial\:x}(4\tan(xy))
derivative of f(x)=tan(2sqrt(x))	derivative\:f(x)=\tan(2\sqrt{x})
tangent of f(x)=xsqrt(x),\at x=36	tangent\:f(x)=x\sqrt{x},\at\:x=36
taylor 1/(1+2x),0	taylor\:\frac{1}{1+2x},0
derivative of (ln(x)((x^7+3)/(x^3-10)))	\frac{d}{dx}((\ln(x))(\frac{x^{7}+3}{x^{3}-10}))
integral of (3x-7)^9	\int\:(3x-7)^{9}dx
integral of 1/(4x^2-9)	\int\:\frac{1}{4x^{2}-9}dx
derivative of 3sin(xcos(x))	\frac{d}{dx}(3\sin(x)\cos(x))
derivative of f(x)=x^{-1}-1/x	derivative\:f(x)=x^{-1}-\frac{1}{x}
derivative of 2/(3x-1)	\frac{d}{dx}(\frac{2}{3x-1})
integral of y^2cos(x)+z^3	\int\:y^{2}\cos(x)+z^{3}dx
f^{''}(x)=4x^2+8x-17	f^{\prime\:\prime\:}(x)=4x^{2}+8x-17
(\partial)/(\partial x)(4x^2+5y^3-3)	\frac{\partial\:}{\partial\:x}(4x^{2}+5y^{3}-3)
(\partial)/(\partial x)(e^xsin(yz))	\frac{\partial\:}{\partial\:x}(e^{x}\sin(yz))
derivative of e^{-0.3x}	\frac{d}{dx}(e^{-0.3x})
(\partial)/(\partial x)(e^{xy}+xye^{xy})	\frac{\partial\:}{\partial\:x}(e^{xy}+xye^{xy})
derivative of (ax^3+bx+c/(dx^3-e))	\frac{d}{dx}(\frac{ax^{3}+bx+c}{dx^{3}-e})
integral from 0 to 1 of (6+x)/(1+x^2)	\int\:_{0}^{1}\frac{6+x}{1+x^{2}}dx
tangent of f(x)=(x^3)/(x+1),\at x=1	tangent\:f(x)=\frac{x^{3}}{x+1},\at\:x=1
derivative of tan(pix-1+e^{cos(x)})	\frac{d}{dx}(\tan(πx-1)+e^{\cos(x)})
derivative of y=(x-1)^3	derivative\:y=(x-1)^{3}
integral of tan(x)ln(cos(x))	\int\:\tan(x)\ln(\cos(x))dx
integral of (x^2)/(x^2+4)	\int\:\frac{x^{2}}{x^{2}+4}dx
area y=x^2-1,y=2x-1,y=x+1	area\:y=x^{2}-1,y=2x-1,y=x+1
tangent of y= 2/(1+x^2),(3,0.2)	tangent\:y=\frac{2}{1+x^{2}},(3,0.2)
x((dy)/(dx))-y=x^5+1	x(\frac{dy}{dx})-y=x^{5}+1
derivative of f(x)=x^2-5x	derivative\:f(x)=x^{2}-5x
limit as x approaches 0+of 8sin(x)ln(x)	\lim\:_{x\to\:0+}(8\sin(x)\ln(x))
integral of (2x+1)/((x^2+x+1)^{3/2)}	\int\:\frac{2x+1}{(x^{2}+x+1)^{\frac{3}{2}}}dx
integral of 1/(6x+1)	\int\:\frac{1}{6x+1}dx
integral from 0 to 1/2 of 2/(1+4x^2)	\int\:_{0}^{\frac{1}{2}}\frac{2}{1+4x^{2}}dx
y^'=(2x(y-1))/(x^2+3)	y^{\prime\:}=\frac{2x(y-1)}{x^{2}+3}
integral of 19sin^3(x)cos^2(x)	\int\:19\sin^{3}(x)\cos^{2}(x)dx
tangent of f(x)= 6/(x^2),\at x=1	tangent\:f(x)=\frac{6}{x^{2}},\at\:x=1
y^{''}-3y^'-10y=0	y^{\prime\:\prime\:}-3y^{\prime\:}-10y=0
taylor 1/((1+x)^2),1	taylor\:\frac{1}{(1+x)^{2}},1
derivative of 5x	\frac{d}{dx}(5x)
integral of 4x^2+1	\int\:4x^{2}+1dx
(\partial)/(\partial x)(x^2-4xy+y^2+6y+3)	\frac{\partial\:}{\partial\:x}(x^{2}-4xy+y^{2}+6y+3)
integral of tan^5(x)sec^{11}(x)	\int\:\tan^{5}(x)\sec^{11}(x)dx
limit as x approaches 0 of 2x*sin(x)	\lim\:_{x\to\:0}(2x\cdot\:\sin(x))
tangent of y=x^2+x,\at x=-2	tangent\:y=x^{2}+x,\at\:x=-2
integral from 0.5 to t+4 of 3	\int\:_{0.5}^{t+4}3dx
integral from-1 to 3 of (4-2x)	\int\:_{-1}^{3}(4-2x)dx
integral from 0 to 9 of k(9-x)	\int\:_{0}^{9}k(9-x)
derivative of arctan((a^2-x^3/(b^2)))	\frac{d}{dx}(\arctan(\frac{a^{2}-x^{3}}{b^{2}}))
derivative of sqrt(x)*(x^5+x^4+3x+2)	\frac{d}{dx}(\sqrt{x}\cdot\:(x^{5}+x^{4}+3x+2))
(\partial ^2)/(\partial {K)(b)\partial b}(a{K}(b)(b)^aL^b)	\frac{\partial\:^{2}}{\partial\:{K}(b)\partial\:b}(a{K}(b)(b)^{a}L^{b})
(dy)/(dx)-6xy=sin(x^2)	\frac{dy}{dx}-6xy=\sin(x^{2})
derivative of (4x/((3x^2-1)^2))	\frac{d}{dx}(\frac{4x}{(3x^{2}-1)^{2}})
integral of 4x-3x^2	\int\:4x-3x^{2}dx
laplacetransform f(t)=t(sin(9t)+e^{-2t})	laplacetransform\:f(t)=t(\sin(9t)+e^{-2t})
integral from 0 to pi of sin^2(6x)	\int\:_{0}^{π}\sin^{2}(6x)dx
(\partial)/(\partial x)(x(x+3y+2))	\frac{\partial\:}{\partial\:x}(x(x+3y+2))
(dy)/(dx)=20+28x+40y+56xy	\frac{dy}{dx}=20+28x+40y+56xy
integral of 5/x	\int\:\frac{5}{x}dx
derivative of g(x)=sqrt(6x+8)	derivative\:g(x)=\sqrt{6x+8}
integral of 2x-y	\int\:2x-ydx
x^2y^'+y^'=xy	x^{2}y^{\prime\:}+y^{\prime\:}=xy
area y=x^2+30x+225,y=17(x+15)	area\:y=x^{2}+30x+225,y=17(x+15)
integral of (5x-2)/(x^2+6x+8)	\int\:\frac{5x-2}{x^{2}+6x+8}dx
y^{''}-4y=6e^{(-t)},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}-4y=6e^{(-t)},y(0)=0,y^{\prime\:}(0)=0
xy^'-y+2=0	xy^{\prime\:}-y+2=0
integral of (2sin(x)-3cos(x))	\int\:(2\sin(x)-3\cos(x))dx
laplacetransform 20t^2	laplacetransform\:20t^{2}
limit as x approaches 17 of x^2-3x+1	\lim\:_{x\to\:17}(x^{2}-3x+1)
derivative of 1/3 (x^2+2)^{3/2}	derivative\:\frac{1}{3}(x^{2}+2)^{\frac{3}{2}}
integral of (256)/(x^3-16x^2)	\int\:\frac{256}{x^{3}-16x^{2}}dx
derivative of 4x+7	\frac{d}{dx}(4x+7)
inverse oflaplace 1/(s^4-9)	inverselaplace\:\frac{1}{s^{4}-9}
inverse oflaplace 1/((s+1)(s^2+5))	inverselaplace\:\frac{1}{(s+1)(s^{2}+5)}
derivative of (sin(2x))/(e^{x^2)}	derivative\:\frac{\sin(2x)}{e^{x^{2}}}
(dy)/(dx)= y/x+3x+5	\frac{dy}{dx}=\frac{y}{x}+3x+5
limit as x approaches-7 of-4x	\lim\:_{x\to\:-7}(-4x)
derivative of (x^2+x-2/(x^2-3x+4))	\frac{d}{dx}(\frac{x^{2}+x-2}{x^{2}-3x+4})
integral of (2x+3)/(x^2+3x)	\int\:\frac{2x+3}{x^{2}+3x}dx
(\partial)/(\partial x)(e^{(x+y)})	\frac{\partial\:}{\partial\:x}(e^{(x+y)})
(\partial)/(\partial x)(10xy-16x)	\frac{\partial\:}{\partial\:x}(10xy-16x)
derivative of 0.5x	\frac{d}{dx}(0.5x)
limit as x approaches-3-of g(x)	\lim\:_{x\to\:-3-}(g(x))
derivative of (6x^2+4x+4/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+4x+4}{\sqrt{x}})
limit as x approaches pi/2 of sec(x)	\lim\:_{x\to\:\frac{π}{2}}(\sec(x))
limit as x approaches 0+of ln(x)*tan(x)	\lim\:_{x\to\:0+}(\ln(x)\cdot\:\tan(x))
x(dy)/(dx)+2y=2e^x	x\frac{dy}{dx}+2y=2e^{x}
inverse oflaplace 5/(pis^2)	inverselaplace\:\frac{5}{πs^{2}}
tangent of 8e^x	tangent\:8e^{x}
y^'+(3y)/x =-1/x	y^{\prime\:}+\frac{3y}{x}=-\frac{1}{x}
(\partial)/(\partial x)(2x^3+xy^2)	\frac{\partial\:}{\partial\:x}(2x^{3}+xy^{2})
1/x (dy)/(dx)=e^{x+y}	\frac{1}{x}\frac{dy}{dx}=e^{x+y}
derivative of 1/(2xsqrt(ln(x+1)))	\frac{d}{dx}(\frac{1}{2x\sqrt{\ln(x)+1}})
integral of cot^3(x)*csc^3(x)	\int\:\cot^{3}(x)\cdot\:\csc^{3}(x)dx
sum from n=1 to infinity of (2n!)/(n^n)	\sum\:_{n=1}^{\infty\:}\frac{2n!}{n^{n}}
derivative of sqrt(r)(2r+1)	derivative\:\sqrt{r}(2r+1)
(dy)/(dt)=5(y-t^2)	\frac{dy}{dt}=5(y-t^{2})
integral of (x^3)/((2+x^4)^9)	\int\:\frac{x^{3}}{(2+x^{4})^{9}}dx

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