What is the integral of (sin(3t+10))/(cos^2(3t+10)) ?

The integral of (sin(3t+10))/(cos^2(3t+10)) is 1/3 sin(3t+10)tan(3t+10)+1/3 cos(3t+10)+C

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integral of (sin(3t+10))/(cos^2(3t+10))

\int \frac{sin ( 3 t + 10 )}{cos ^{2} ( 3 t + 10 )} d t

\frac{1}{3} sin (3 t + 10) tan (3 t + 10) + \frac{1}{3} cos (3 t + 10) + C

Solution steps

\int \frac{sin ( 3 t + 10 )}{cos ^{2} ( 3 t + 10 )} d t

Apply Integration By Parts

: sin (3 t + 10) (- \frac{10}{3} + \frac{1}{3} tan (3 t + 10)) - \int - 10 cos (3 t + 10) + sin (10 + 3 t) d t

= sin (3 t + 10) (- \frac{10}{3} + \frac{1}{3} tan (3 t + 10)) - \int - 10 cos (3 t + 10) + sin (10 + 3 t) d t

\int - 10 cos (3 t + 10) + sin (10 + 3 t) d t = - \frac{10}{3} sin (3 t + 10) - \frac{1}{3} cos (10 + 3 t)

= sin (3 t + 10) (- \frac{10}{3} + \frac{1}{3} tan (3 t + 10)) - (- \frac{10}{3} sin (3 t + 10) - \frac{1}{3} cos (10 + 3 t))

Simplify

sin (3 t + 10) (- \frac{10}{3} + \frac{1}{3} tan (3 t + 10)) - (- \frac{10}{3} sin (3 t + 10) - \frac{1}{3} cos (10 + 3 t)) : \frac{1}{3} sin (3 t + 10) tan (3 t + 10) + \frac{1}{3} cos (3 t + 10)

= \frac{1}{3} sin (3 t + 10) tan (3 t + 10) + \frac{1}{3} cos (3 t + 10)

Add a constant to the solution

= \frac{1}{3} sin (3 t + 10) tan (3 t + 10) + \frac{1}{3} cos (3 t + 10) + C

\frac{d}{d x} (2 x ln (x))

(x - y - 1)^{3} = x, (1, - 1)

y^{^{''}} + y^{^{'}} = 3 sin (4 x)

n \to \infty lim ((n!)^{n})

\int (\frac{2 x + 7}{x ^{2} + 2 x + 5}) d x

What is the integral of (sin(3t+10))/(cos^2(3t+10)) ?
The integral of (sin(3t+10))/(cos^2(3t+10)) is 1/3 sin(3t+10)tan(3t+10)+1/3 cos(3t+10)+C