What is the integral of s^{1/5}cos(s^{6/5}+3) ?

The integral of s^{1/5}cos(s^{6/5}+3) is 5/6 sin(s^{6/5}+3)+C

Popular >

integral of s^{1/5}cos(s^{6/5}+3)

\int s^{\frac{1}{5}} cos (s^{\frac{6}{5}} + 3) d s

\frac{5}{6} sin (s^{\frac{6}{5}} + 3) + C

Solution steps

\int s^{\frac{1}{5}} cos (s^{\frac{6}{5}} + 3) d s

Apply u-substitution

: \int \frac{5 cos ( u )}{6} d u

= \int \frac{5 cos ( u )}{6} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{5}{6} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{5}{6} sin (u)

Substitute back

u = s^{\frac{6}{5}} + 3

= \frac{5}{6} sin (s^{\frac{6}{5}} + 3)

Add a constant to the solution

= \frac{5}{6} sin (s^{\frac{6}{5}} + 3) + C

\int 1 - \frac{3}{x ^{2} + 3} d x

\int (x^{3} + 8)^{5} 3 x^{2} d x

\int 2 e^{0.2 x} d x

\int \frac{x}{( 3 x + 1 ) ^{2}} d x

\int 4 x + 8 d x

What is the integral of s^{1/5}cos(s^{6/5}+3) ?
The integral of s^{1/5}cos(s^{6/5}+3) is 5/6 sin(s^{6/5}+3)+C